Question

let (f(x)=-4x^{2}-20x + 2). find the (x)-value(s) where the graph of the function has a horizontal tangent line. separate multiple answers with commas. enter dne if there are no such (x).

Explanation:

Step1: Find the derivative

The derivative of $f(x)=-4x^{2}-20x + 2$ using the power - rule $\frac{d}{dx}(ax^{n})=nax^{n - 1}$ is $f'(x)=-8x-20$.

Step2: Set the derivative equal to zero

A horizontal tangent line occurs where the slope of the function (the derivative) is zero. So we set $f'(x)=0$.
$-8x - 20=0$.

Step3: Solve for x

Add 20 to both sides: $-8x=20$.
Then divide both sides by - 8: $x=-\frac{20}{8}=-\frac{5}{2}$.

Answer:

$x =-\frac{5}{2}$