Question

The derivative of $f(x)=\frac{x^4}{3}-\frac{x^5}{5}$ attains its maximum value at $x$ equal to

• A. $\frac{4}{3}$
• B. $\frac{5}{3}$
• C. 1
• D. 0

Answer 1

Answer: (C)

$f^{\prime }(x)=\frac{4}{3}{x}^3-x^4$
$f^{\prime \prime }(x)=4x^2-4x^3=4x^2(1-x)=0$
$\therefore x=1$
$f^{\prime \prime \prime }(x)=8x-12x^2$
$\therefore f{}^{\prime \prime \prime }(1)=-4<0$