Question

Find the absolute extrema if they exist, as well as all values of x where they occur, for the function $f(x) = 3x^3 + 12x^2 + 12x - 5$ on the domain $[-4, 0]$. Find the derivative of $f(x) = 3x^3 + 12x^2 + 12x - 5$. $f'(x) = 9x^2 + 24x + 12$

          Find the absolute extrema if they exist, as well as all values of x where they occur, for the function $f(x) = 3x^3 + 12x^2 + 12x - 5$ on the domain $[-4, 0]$.
Find the derivative of $f(x) = 3x^3 + 12x^2 + 12x - 5$.
$f'(x) = 9x^2 + 24x + 12$

Find the absolute extrema if they exist, as well as all values of x where they occur, for the function f(x) = 3x^3 + 12x^2 + 12x - 5 on the domain [-4, 0].
Find the derivative of f(x) = 3x^3 + 12x^2 + 12x - 5.
f'(x) = 9x^2 + 24x + 12

Added by Natalie C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Tim Thornhill

07/13/2023

Step 1

Setting f'(x) = 9x^2 + 24x + 12 equal to zero: 9x^2 + 24x + 12 = 0 Dividing by 3 to simplify: 3x^2 + 8x + 4 = 0 Factoring: (3x + 2)(x + 2) = 0 Setting each factor to zero: 3x + 2 = 0 or x + 2 = 0 x = -2/3 or x = -2 Show more…

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Find the absolute extrema if they exist, as well as all values of x where they occur, for the function f(x) = 3x^3 + 12x^2 + 12x - 5 on the domain [-4, 0]. Find the derivative of f(x) = 3x^3 + 12x^2 + 12x - 5. f'(x) = 9x^2 + 24x + 12 Find the absolute extrema if they exist, as well as all values of x where they occur, for the function f(x) = 3x^3 + 12x^2 + 12x - 5 on the domain [-4, 0]. Find the derivative of f(x) = 3x^3 + 12x^2 + 12x - 5. f'(x) = 9x^2 + 24x + 12