Question

Find the equation of a line passing through the same point that f(x) passes through at x = 3 with a slope equal to the limit you found in part a.

Answer 1

The function is f(x) = x³ − 4x² + 2. Then the slope at x = 3 of the function will be 3.

How to find the slope?

The slope of a line or straight object is the ratio of how much amount of rise occurs in correspondence to the increment in the run.

Thus, we get:

Slope = rise/ run

The function is given below.

f(x) = x³ − 4x² + 2

A line passing through the same point that f(x) passes through at x = 3 with a slope equal to the limit.

Then the slope of the function is given by the differentiation. Then we have

$\rm Slope|_3 = \dfrac{d}{dx} f(x)\\\\Slope|_3 = \dfrac{d}{dx} (x^3 - 4x ^2 + 2)$

Slope|₃ = 3x² − 8x

Slope|₃ = 3(3)² − 8(3)

Slope|₃ = 27 − 24

Slope|₃ = 3

Learn more about the slope here:

brainly.com/question/2503591

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