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What is the meaning of continuous first derivatives of a function?
Wiki User
∙ 12y ago
A continuous function is one where there are no discontinuities or step changes in the function, i.e. for a small change in input value, as that small change approaches zero, there is a progressively smaller change in output value.
There are many definitions, some formal and some intuitive, for continuous functions. The definition given above is intuitive.
The same definition can be give to the deriviatives or the integrals of a function. Continousness does not depend on being a deriviative or integral.
Wiki User
∙ 12y ago
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Can you please show that first derivation is piecewise continuous?
Assuming you mean "derivative", I believe it really depends on the function. In the general case, there is no guarantee that the first derivative is piecewise continuous, or that it is even defined.
What is the function if the first derivative of a function is a constant?
A linear function, for example y(x) = ax + b has the first derivative a.
What if the fourth derivative of a polynomial is zero?
There are many things that can be said about a polynomial function if its fourth derivative is zero, but the main thing you can know about this function from this information is that its order is 3 or less. Consider an nth order polynomial with only positive exponents: axn + bxn-1 + ... + cx2 + dx + e As you derive this function, its derivatives will eventually be equal to zero. The number of derivatives that are nonzero before they all become zero can tell you what order the polynomial function was. Consider an example, y = x4. y = x4 y' = 4x3 y'' = 12x2 y''' = 24x y(4) = 24 y(5) = 0 The original polynomial was of order 4, and its derivatives were nonzero up until its fifth derivative. From this, you can generalize to say that any function whose fifth derivative is equal to zero is of order 4 or less. If the function was of higher order than 4, its derivatives would not become zero until later. If the function was of lower order than 4, its fifth derivative would still be zero, but it would not be the first zero-valued derivative. So this experimentation yielded a rule that the first zero-valued derivative is one greater than the order of the polynomial. Your problem states that some polynomial has a fourth derivative that is zero. Our working rule states that this polynomial can be of highest order 3. So, your polynomial can be, at most, of the form: y = ax3 + bx2 + cx + d Letting the constants a through d be any real number (including zero), this general form expresses any polynomial that will satisfy your condition.
What is the difference between differentiation and integration?
Differentiation involves determination of the slope, i.e. the derivative, of a function. The slope of a function at a point is a straight line that is tangent to that function at that point, and is the line defined by the limit of two points on the original curve, one of those two points being the point in question, as their distance between each other becomes zero. There are several things you can do with derivatives, not the least of which is aid in plotting functions and finding various minima and maxima. Integration involves determination of the inverse-slope, i.e. the integral, of a function. The integral of a function is another function whose derivative is the first function. There are several things you can do with integrals, not the least of which is finding the area or volume under or in a curve or shape.
How do you calculate critical points of derivatives?
The "critical points" of a function are the points at which the derivative equals zero or the derivative is undefined. To find the critical points, you first find the derivative of the function. You then set that derivative equal to zero. Any values at which the derivative equals zero are "critical points". You then determine if the derivative is ever undefined at a point (for example, because the denominator of a fraction is equal to zero at that point). Any such points are also called "critical points". In essence, the critical points are the relative minima or maxima of a function (where the graph of the function reverses direction) and can be easily determined by visually examining the graph.
What is well behaved wave function?
List of the characteristics a well-behaved wave function are ..The function must be single-valued; i.e. at any point in space, the function must have only one numerical value.The function must be finite and continuous at all points in space. The first and second derivatives of the function must be finite and continuous.The function must have a finite integral over all space.
What characteristics of the graph of a function by using the concept of differentiation first and second derivatives?
If the first derivative of a function is greater than 0 on an interval, then the function is increasing on that interval. If the first derivative of a function is less than 0 on an interval, then the function is decreasing on that interval. If the second derivative of a function is greater than 0 on an interval, then the function is concave up on that interval. If the second derivative of a function is less than 0 on an interval, then the function is concave down on that interval.
Why does your body require a continuous amount of oxygen?
first so you wont die and the cells need to to function properly
What is the relationship between the Green's Theorem Divergence Theorem and Stoke's Theorem?
GREEN'S THEOREM: if m=m(x,y) and n= n(x,y) are the continuous functions and also partial differential in a region 'r' of x,y plane bounded by a simple closed curve c. DIVERGENCE THEOREM: if f is a vector point function having continuous first order partial derivatives in the region v bounded by a closed curve s
What words are derivatives of 'tera-'?
Derivatives of the prefixed syllables 'tera-' fall into one of three groups in terms of meaning. One group includes derivatives that mean 'three', which is the meaning of the Greek prefix 'ter-'. A second group includes derivatives that mean 'trillion', which is the meaning of the Greek prefix 'tera-'. For example, the noun terabit refers to one million million binary digits of information. The noun terahertz refers to one trillion hertz. A third group includes derivatives that refer to monsters and monstrosities, which is the meaning of the Greek prefix 'terat-'. For example, the noun teratogen refers to an agent that malforms the foetus in the first three months of pregnancy. The adjective teratoidrefers to someone or something that's abnormally formed. And the noun teratology is the study of malformations and monstrosities.
What is normalising a wave function?
A wave function is normalized by determining normalization constants such that both the value and first derivatives of each segment of the wave function match at their intersections. If instead you meant renormalization, that is a different problem having to do with elimination of infinities in certain wave functions.
What has the author M J D Powell written?
M J D. Powell has written: 'A Fortran subroutine for unconstrained minimization, requiring first derivatives of the objective function'
How does this meaning relate to the location and function of an atrium in the heart?
first pump
Can you please show that first derivation is piecewise continuous?
Assuming you mean "derivative", I believe it really depends on the function. In the general case, there is no guarantee that the first derivative is piecewise continuous, or that it is even defined.
What statement must you write before differentiating from first principles to show your knowledge of the topic?
You should generally state that the function is continuous and differentiable over the interval you are using (or throughout the entire function).
What is the formula of bordered Hessian matrix?
The bordered hessian matrix is used for fulfilling the second-order conditions for a maximum/minimum of a function of real variables subject to a constraint. The first row and first column of the bordered hessian correspond to the derivatives of the constraint whereas the other entries correspond to the second and cross partial derivatives of the real-valued function. Other than the bordered entries, the main diagonal of the sub matrix consists of entries for the second partial derivatives. All other entries of the sub matrix off of the main diagonal correspond to all combinations of cross partials. Evaluating the determinant of the bordered hessian will allow one to determine if the function attains its maximum or minimum at the stationary points, which by the way are limited in the fact that they must both satisfy the gradient equations and the constraint.
Who invented the first continuous cement mixer?
Randy Adams of Spur Tx has the first known usable continuous portable mixer
