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

Answer 1

#9#

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.

Let's begin. We have #y=5x-x^2#. Using the power rule, we find the derivative is #y'=5-2x#
Next step is to find what this is when #x=-2#: #y'=5-2(-2)# #y'=5+4# #y'=9#
Therefore, our derivative (instantaneous rate of change) at #x=-2# is #9#.
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Answer 2

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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Answer from HIX Tutor

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.

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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