2 multiple choice 1 point graph of f the figure above shows the graph of the polynomial function f. for…
2 multiple choice 1 point graph of f the figure above shows the graph of the polynomial function f. for which value of x is it true that f(x)<f(x)<f(x)? (a) a (b) b (c) c (d) d (e) e a b c d e previous
Answer
Answer:
B. $b$
Explanation:
Step1: Analyze $f(x)$ at $x = b$
$f(b)>0$ as the function is above - the - $x$ - axis at $x = b$.
Step2: Analyze $f'(x)$ at $x = b$
$f'(b)=0$ since the function has a horizontal tangent at $x = b$.
Step3: Analyze $f''(x)$ at $x = b$
$f''(b)<0$ because the function is concave - down at $x = b$.
Step4: Compare the values
We have $f''(b)<f'(b)<f(b)$ since $f''(b)<0$, $f'(b) = 0$, and $f(b)>0$.