# How do you find the instantaneous rate of change of the function #y= 5x - x^2# when x=-2?

The derivative of a function, or how quickly the function is changing, is the mathematical representation of the instantaneous rate of change, which is the rate at which something is going at a given point in time.

We only need to take our function's derivative, evaluate it at the relevant point, and we're done finding the instantaneous rate of change.

By signing up, you agree to our Terms of Service and Privacy Policy

To find the instantaneous rate of change of the function y = 5x - x^2 when x = -2, you would first find the derivative of the function with respect to x, which represents the rate of change of the function at any given point. Then, you would substitute x = -2 into the derivative to find the instantaneous rate of change at that specific point.

The derivative of the function y = 5x - x^2 is given by dy/dx = 5 - 2x.

Substituting x = -2 into the derivative, we get dy/dx = 5 - 2(-2) = 5 + 4 = 9.

So, the instantaneous rate of change of the function y = 5x - x^2 when x = -2 is 9.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What is the equation of the line tangent to #f(x)=(x+6)^2-7x # at #x=-1#?
- What is the equation of the line normal to # f(x)=(2x-2)^2+4x# at # x=-3#?
- How do you find the points where the graph of the function # f (x) = 3 x^ 3 + 8 x^ 2 + 4 x + 7 # has horizontal tangents and what is the equation?
- What is the equation of the line that is normal to #f(x)= e^(2x-2) # at # x= 1 #?
- How do you use the limit definition of a derivative to take the derivative of #f(x) = sin(nx)# for a constant n?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7