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When was function not having a derivative at a point?
Definition: A function f is differentiable at a if f'(a) exists. it is differentiable on an open interval (a, b) [or (a, ∞) or (-∞, a) or (-∞, ∞)]if it is differentiable at every number in the interval.Example: Where is the function f(x) = |x| differentiable?Answer:1. f is differentiable for any x > 0 and x < 0.2. f is not differentiable at x = 0.That's mean that the curve y = |x| has not a tangent at (0, 0).Thus, both continiuty and differentiability are desirable properties for a function to have. These properties are related.Theorem: If f is differentiable at a, then f is continuous at a.The converse theorem is false, that is, there are functions that are continuous but not differentiable. (As we saw at the example above. f(x) = |x| is contionuous at 0, but is not differentiable at 0).The three ways for f not to be differentiable at aare:a) if the graph of a function f has a "corner" or a "kink" in it,b) a discontinuity,c) a vertical tangent
How do you differentiate a fraction with x as a numerator?
Suppose you wish to differentiate x/f(x) where f(x) is a differentiable function of x, and writing f for f(x) and f'(x) for the derivative of f(x), d/dx (x/f) = [f - x*f']/(f2)
What is holomorphic function?
A holomorphic function is a function that is differentiable at every point on its domain. In order for it to be differentiable, it needs to satisfy the Cauchy-Riemann equation properties, such that: f(z) = u(x,y) + iv(x,y) ux = vy vx = -uy If that is so, then f'(z) = ux + ivx Otherwise, if a function doesn't satisfy these conditions, we say that it's not holomorphic. For instance: f(z) = z̅ Test with the following properties: ux = vy vx = -uy z̅ is written as u(x,y) - iv(x,y). Take the partial derivatives of u(x,y) and v(x,y). Then: ux = -vy vx = -(-uy) = uy Since the conditions don't hold, that function is not holomorphic.
How do you write the rule for a sequence?
You can write it as Un or f(n) equal to some function of n, where the function can be anything at all.
What does it mean when f is differentiable at x equals 2?
what does it mean when f(x) is differentiable along an interval?it means that f is continuous along that domain. In other words, the curve f is smooth and does not break at any point along the interval.what does it mean when f(x) is differentiable at a point c?It means that f is continuous above the domain given by the interval that is an infinitesimally small distance from c. In other words the curve, f(x), is smooth and does not break along the differentially small interval given by c and at all of the values unimaginably close to c.what does it mean when the derivative of f(x) at c equals 2?It means that the instantaneous rate of change (slope) of f(x) at that point is equal to 2.what does it mean when the derivative of f(x) everywhere along an interval equals 2?It means that every single point along that interval has the same slope of 2. In other words, that interval yields a line with a slope of 2.
What is the derivative of modulus of x?
Well.. this is the formula to get the derivative of the modulus - d|f(x)|/dx = [ |f(x)|/f(x) ] * f'(x)
When was function not having a derivative at a point?
Definition: A function f is differentiable at a if f'(a) exists. it is differentiable on an open interval (a, b) [or (a, ∞) or (-∞, a) or (-∞, ∞)]if it is differentiable at every number in the interval.Example: Where is the function f(x) = |x| differentiable?Answer:1. f is differentiable for any x > 0 and x < 0.2. f is not differentiable at x = 0.That's mean that the curve y = |x| has not a tangent at (0, 0).Thus, both continiuty and differentiability are desirable properties for a function to have. These properties are related.Theorem: If f is differentiable at a, then f is continuous at a.The converse theorem is false, that is, there are functions that are continuous but not differentiable. (As we saw at the example above. f(x) = |x| is contionuous at 0, but is not differentiable at 0).The three ways for f not to be differentiable at aare:a) if the graph of a function f has a "corner" or a "kink" in it,b) a discontinuity,c) a vertical tangent
Where is f(x) discontinuous but not differentiable Explain?
Wherever a function is differentiable, it must also be continuous. The opposite is not true, however. For example, the absolute value function, f(x) =|x|, is not differentiable at x=0 even though it is continuous everywhere.
Definition of Differentiable function?
Let f be a function with domain D in R, the real numbers, and D is an open set in R. Then the derivative of f at the point c is defined as: f'(c) =lim as x-> c of the difference quotient [f(x)-f(c)]/[x-c] If that limit exits, the function is called differentiable at c. If f is differentiable at every point in D then f is called differentiable in D.
What is the function which derrivative not possible?
A function f(x) is not differentiable at x=a if: lim h-->0 [f(a+h)-f(a)] / h does not exist.
The function f is given by f of x equals x to the 3 plus 12x minus 24 is?
A cubic function, continuous, differentiable.
What is an example of how a modulus function works?
In mathematics, the modulus of a real number is its numerical value without regard to its sign. So, for example, 3 is the absolute value of both 3 and −3. When graphing a modulus function, f(|x|), graph the function f(x) ignoring the modulus and simply reflect any values below the x-axis (negative values) so they become positive.
Let f be an odd function with antiderivative F. Prove that F is an even function. Note we do not assume that f is continuous or even integrable.?
An antiderivative, F, is normally defined as the indefinite integral of a function f. F is differentiable and its derivative is f.If you do not assume that f is continuous or even integrable, then your definition of antiderivative is required.
Can a graph be differentiable at a specific point but not continuous at the same point?
Not according to the usual definitions of "differentiable" and "continuous".Suppose that the function f is differentiable at the point x = a.Then f(a) is defined andlimit (h -> 0) [f(a+h) - f(a)]/h exists (has a finite value).If this limit exists, then it follows thatlimit (h -> 0) [f(a+h) - f(a)] exists and equals 0.Hence limit (h -> 0) f(a+h) exists and equals f(a).Therefore f is continuous at x = a.
When does the derivative of a function exist at a given point?
Let f be a function and a be the given point you are considering. Then,f(x) - f(a)---------------(x-a)is the difference quotient. If the limit as x approaches a exists, then the function is differentiable at a, or we say the derivative exists at a. If that limit does not exist, then the derivative does not exist at that point.
How do you differentiate a fraction with x as a numerator?
Suppose you wish to differentiate x/f(x) where f(x) is a differentiable function of x, and writing f for f(x) and f'(x) for the derivative of f(x), d/dx (x/f) = [f - x*f']/(f2)
What is an example of a function that is continuous on the interval a b for which the conclusion of the mean value theorem does not hold?
Let f(x)=abs(x) , absolute value of x defined on the interval [5,5] f(x)= |x| , -5 ≤ x ≤ 5 Then, f(x) is continuous on [-5,5], but not differentiable at x=0 (that is not differentiable on (-5,5)). Therefore, the Mean Value Theorem does not hold.
