Find the absolute maximum of the function $f ( x ) = x ^ { 3 }$ on the interval $- \frac { 1 } { 2 } \leq x \leq 1$ .
A)1
B)-1
C)0
D) $\frac { 1 } { 8 }$

Question

Quizplus · Accepted Answer

The function $f(x) = x^3$ is increasing on the entire real line because its derivative $f'(x) = 3x^2$ is always non-negative. Therefore, the absolute maximum on the interval $-\frac{1}{2} \leq x \leq 1$ occurs at the right endpoint, $x = 1$, giving $f(1) = 1^3 = 1$.

Find the Absolute Maximum of the Function f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3

Find the Absolute Maximum of the Function $f ( x ) = x ^ { 3 }$