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Assuming function of one variable...
Want y[x] s.t. y''[x] =y[x]
The characteristic equation is r^2 = 1.
r = (+/-) 1
So, e^(x*1) and e^(x * -1) work. To get full generality, multiply them by any constants A,B and add.
y[x] = A e^x + B e ^(-x)
y'[x] = A e^x - B e ^(-x)
y''[x] = A e^x + B e ^(-x) = y[x]
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How can you know that a value is the minimum of a function?
When the first derivative of the function is equal to zero and the second derivative is positive.
To find critical points?
Take the derivative of the function and set it equal to zero. The solution(s) are your critical points.
What is a derivative graph?
A derivative graph tracks the slope of a function.
What is the name for values of an independent variable for a function that make its derivative equal to 0 or not defined but are not within the domain of the original function?
That sounds a lot like a critical point to me.
What is the derivative of 3cosx?
The derivative of 3cos(x) is -3sin(x). This can be found using the chain rule, which states that the derivative of a composition of functions is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function. In this case, the derivative of cos(x) is -sin(x), and when multiplied by the constant 3, we get -3sin(x) as the derivative of 3cos(x).
How can you know that a value is the minimum of a function?
When the first derivative of the function is equal to zero and the second derivative is positive.
How do you find second derivative of a function?
All it means to take the second derivative is to take the derivative of a function twice. For example, say you start with the function y=x2+2x The first derivative would be 2x+2 But when you take the derivative the first derivative you get the second derivative which would be 2
Where the graph of a function equals the value zero?
you have to first find the derivative of the original function. You then make the derivative equal to zero and solve for x.
What is the second derivative of a function's indefinite integral?
well, the second derivative is the derivative of the first derivative. so, the 2nd derivative of a function's indefinite integral is the derivative of the derivative of the function's indefinite integral. the derivative of a function's indefinite integral is the function, so the 2nd derivative of a function's indefinite integral is the derivative of the function.
What is the difference between differential and derivative in the field of calculus?
The derivative refers to the rate at which a function changes with respect to another measure. The differential refers to the actual change in a function across a parameter. The differential of a function is equal to its derivative multiplied by the differential of the independent variable . The derivative of a function is the the LIMIT of the ratio of the increment of a function to the increment of the independent variable as the latter tends to zero.
How do you find the minimum and maximum points of a function?
Set the first derivative of the function equal to zero, and solve for the variable.
Is signum function differentiable?
The signum function, also known as the sign function, is not differentiable at zero. This is because the derivative of the signum function is not defined at zero due to a sharp corner or discontinuity at that point. In mathematical terms, the signum function has a derivative of zero for all values except at zero, where it is undefined. Therefore, the signum function is not differentiable at zero.
What is the derivative of the absolute value of x?
The function is called the signum function, or sign(x). It is equal to abs(x)/x
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.
How do you find the Min value for y in this equation?
You didn't specify the equation. A minimum or maximum value of a function is often found by calculating the derivative of a function, writing an equation for derivative equal to zero, and then analyzing points where the derivative either doesn't exist, or is equal to zero. You'll find find information about this in introductory calculus books.
What you say if a function whose derivative and antiderivative is same?
That means that either the function is equal to zero everywhere (y = 0), or it is the exponential function (y = ex).
What does it mean for a function when the graph of the derivative crosses the x-axis?
This means that the function has reached a local maximum or minimum. Since the graph of the derivative crosses the x-axis, then this means the derivative is zero at the point of intersection. When a derivative is equal to zero then the function has reached a "flat" spot for that instant. If the graph of the derivative crosses from positive x to negative x, then this indicates a local maximum. Likewise, if the graph of the derivative crosses from negative x to positive x then this indicates a local minimum.
