# 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.

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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.

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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.

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