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garik1379 [7]
10 months ago
8

I need help!

Mathematics
1 answer:
arsen [322]10 months ago
7 0

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

<h3>What is the instantaneous rate of change of the function at the given point?</h3>

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

#SPJ1

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<u>Step 1: Define equation</u>

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