Question

Let $f\left(x\right)=x^5-x^3+x+2,x\epsilon [-1,1]$ then

• A. Maximum value of $f\left(x\right)$ is 3
• B. Maximum value of $f\left(x\right)$ is 7
• C. Minimum value of $f\left(x\right)$ is zero
• D. Minimum value of $f\left(x\right)$ equals -1

Answer 1

The correct option is A Maximum value of $f\left(x\right)$ is 3

$f\left(x\right)=x^5-x^3+x+2$
$f^{\prime }\left(x\right)=5x^4-3x^2+1$
Now discriminant of $5x^4-3x^2+1$ is negative
thus $f^{\prime }\left(x\right)>0$ for all $xϵR$
Hence maximum value of $f\left(x\right)$ will occur at $x=1$ in $xϵ[-1,1]$
which is 3.