The function is f(x) = x³ − 4x² + 2. Then the slope at x = 3 of the function will be 3.
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
[tex]\rm Slope|_3 = \dfrac{d}{dx} f(x)\\\\Slope|_3 = \dfrac{d}{dx} (x^3 - 4x ^2 + 2)[/tex]
Slope|₃ = 3x² − 8x
Slope|₃ = 3(3)² − 8(3)
Slope|₃ = 27 − 24
Slope|₃ = 3
Learn more about the slope here:
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