Question

Find the maximum and minimum values of x³-3x+11

Answer 1

Answer:

Maximum value =13

Minimum value = 9

Step-by-step explanation:

Let $f(x)=x^3-3x+11$

$f '(x)=3x^2-3$

$f ''(x)=6x$

Now,

$f '(x)=0$

$\implies\:3(x^2-1)=0$

$\implies\:x^2-1=0$

$\implies\:x^2=1$

$\implies\:x=1,-1$

At x=1, $f ''(x)=6(1)=6>0$

$\therefore$ f attaains minimum at x=1

Minimum value $=f(1)=1^3-3(1)+11=1-3+11=12-3=9$

At x=-1, $f ''(x)=6(-1)=-6<0$

$\therefore$ f attaains maximum at x=-1

Maximum value $=f(1)=(-1)^3-3(-1)+11=-1+3+11=13$