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Q.
The derivative of $f(x)=\frac{x^4}{3}-\frac{x^5}{5}$ attains its maximum value at $x$ equal to
Continuity and Differentiability
Solution:
$ f ^{\prime}( x )=\frac{4}{3} x ^3- x ^4$
$f ^{\prime \prime}( x )=4 x ^2-4 x ^3=4 x ^2(1- x )=0 $
$\therefore x =1$
$f ^{\prime \prime \prime}( x )=8 x -12 x ^2$
$\therefore f { }^{\prime \prime \prime}(1)=-4<0$