question 6 - 1 point consider the function f(x) below. over what interval is the function concave down? give…

question 6 - 1 point consider the function f(x) below. over what interval is the function concave down? give your answer in interval notation. f(x)=-8x³ - 6x² - 6x - 2 provide your answer below: f(x) is concave down over the interval

question 6 - 1 point consider the function f(x) below. over what interval is the function concave down? give your answer in interval notation. f(x)=-8x³ - 6x² - 6x - 2 provide your answer below: f(x) is concave down over the interval

Answer

Explanation:

Step1: Find first - derivative

Differentiate $f(x)=-8x^{3}-6x^{2}-6x - 2$ using power rule. $f'(x)=-24x^{2}-12x - 6$.

Step2: Find second - derivative

Differentiate $f'(x)$ using power rule. $f''(x)=-48x-12$.

Step3: Set $f''(x)<0$ for concave - down

Solve the inequality $-48x - 12<0$. Add 12 to both sides: $-48x<12$. Divide both sides by - 48 and reverse the inequality sign: $x>-\frac{1}{4}$.

Answer:

$(-\frac{1}{4},\infty)$