Question

Let $f\left(x\right)=8x^5-15x^4+10x^2$. Its point of local maxima is $x=a$
and point of inflexion is $x=b$, $bϵI$ then the value of $2(a+b)$ is

Answer 1

$f\left(x\right)=8x^5-15x^4+10x^2$
$f^{\prime }\left(x\right)=40x^4-60x^3+20x$
$=20x(2x^3-3x^2+1)$
$=20x(x-1{)}^2(2x+1)$
For maxima or minima,
$f^{\prime }\left(x\right)=0$
$\Rightarrow x=0,\frac{1}{2},1$
$f^{\prime \prime }\left(x\right)>0$ at $x=0$
Local maxima occurs at$x=-\frac{1}{2}$
Point of inflexion is $x=1$
$\therefore 2(a+b)=1$