$$ 1

Question

$$ 1< $$ For $$ f(x)=2 x^{4}-8 x^{3}+4 $$ find the following. (A) $$ f^{\prime}(x) $$ (B) The slope of the graph of $$ f $$ at $$ x=-2 $$ (C) The equation of the tangent line at $$ x=-2 $$ (D) The value(s) of $$ x $$ where the tangent line is horizontal (A) $$ f^{\prime}(x)=\square $$

UpStudy AI · Accepted Answer

**Step 1. Differentiate $$ f(x) $$**

Given
$$
f(x)=2x^4-8x^3+4,
$$
differentiate term-by-term:
- The derivative of $$ 2x^4 $$ is $$ 8x^3 $$.
- The derivative of $$ -8x^3 $$ is $$ -24x^2 $$.
- The derivative of the constant $$ 4 $$ is $$ 0 $$.

Thus,
$$
f^\prime(x)=8x^3-24x^2.
$$
$$ f^\prime(x) = 8x^3 - 24x^2 $$

For find the following.
(A)
(B) The slope of the graph of at
© The equation of the tangent line at
(D) The value(s) of where the tangent line is horizontal
(A)

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For find the following. (A) (B) The slope of the graph of at © The equation of the tangent line at (D) The value(s) of where the tangent line is horizontal (A)