Find the absolute maximum of the function $f ( x ) = x ^ { 5 } - x ^ { 4 }$ on the interval -1$\le$ x $\le$ 1.
A) 0
B) 1
C) -1
D) -2

Question

Find the absolute maximum of the function $f ( x ) = x ^ { 5 } - x ^ { 4 }$ on the interval -1$\le$ x $\le$  1.
A) 0
B) 1
C) -1
D) -2

Quizplus · Accepted Answer

The absolute maximum of the function $f(x) = x^5 - x^4$ on the interval $[-1, 1]$ occurs at the endpoints or where the derivative equals zero. The derivative $f'(x) = 5x^4 - 4x^3$ equals zero when $x = 0$ or $x = 4/5$. Evaluating $f(x)$ at $x = -1$, $x = 0$, $x = 4/5$, and $x = 1$, we find $f(-1) = -2$, $f(0) = 0$, $f(4/5) = (4/5)^5 - (4/5)^4 < 1$, and $f(1) = 0$. Therefore, the absolute maximum value on the given interval is $0$.

Find the Absolute Maximum of the Function f(x)=x5−x4f ( x ) = x ^ { 5 } - x ^ { 4 }f(x)=x5−x4

Find the Absolute Maximum of the Function $f ( x ) = x ^ { 5 } - x ^ { 4 }$