Math H.

asked • 10/31/22

Estimate the instantaneous rate of change of the following function...

Estimate the instantaneous rate of change of the function sa034-1.jpg at sa034-2.jpg.


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Grade 12 Advanced Functions

Please write clearly and neatly. Thanks.








Brenda D.

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Math H I have a question are you using derivates in your class? If you are into derivatives in your class, you can take the first derivative with respect to x then plug in -3 you should get 27. I ask about derivatives because, the first derivative using the Power rule should give you derivates term by term for your function.
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10/31/22

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Joseph G. answered • 10/31/22

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Graduate Student and Substitute Teacher / B.A. in Chemistry (3.85 GPA)

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Using calculus you can find the instantaneous rate of change of x = -3 by taking the derivative of the function and plugging in -3 for x. The derivative is f'(x) = 4x3 + 15x2. f'(-3) = 27. However, you could estimate the instantaneous rate of change by finding the slope between two points slightly before and after x = -3 such as x = -2.99 and x = -3.01.

Slope = (y2 - y1) / (x2-x1)

If you use x1 = -3.01, then

y1 = f(-3.01) = (-3.01)4 + 5(-3.01)3 + 2

If you use x2 = -2.99, then

y2 = f(-2.99)

Using these values, you will get a slope or instantaneous rate of change between 26 and 28.

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