Question

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Answer 1

The instantaneous rate of change of the function f(x) = −4x² − 3x + 1 at the point x = -3 is 21.

What is the instantaneous rate of change of the function at the given point?

The instantaneous rate of change is simply the change in the derivative value at a specific point.

Given the data in the question;

• f(x) = −4x² − 3x + 1
• Point x = -3

To determine the instantaneous rate of change of the function, first find the derivative of the function.

f(x) = −4x² − 3x + 1

Applying sum rule, with respect to x

d/dx[ -4x² ] + d/dx[ -3x ] + d/dx[ 1 ]

[ 2 × -4x¹ ] + [ 1 × -3x⁰ ] + d/dx[ 1 ]

[ -8x ] + [ -3 ] + d/dx[ 1 ]

-8x - 3 + d/dx[ 1 ]

Differentiate using constant rule

-8x - 3 + [ 0 ]

-8x - 3

f'(x) = -8x - 3

Next, plug x = -3 into the derivative and simplify.

f'(x) = -8x - 3

f'(-3) = -8(-3) - 3

f'(-3) = 24 - 3

f'(-3) = 21

Therefore, the instantaneous rate of change of the function f(x) = −4x² − 3x + 1 at the point x = -3 is 21.

Learn more about instantaneous rate of change here: brainly.com/question/28122560

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