Question

At what value of x, the function 2x^3/3+2x^2-6x+4 is minimum​

Answer 1

x=1

Explanation:

We are given that

`(2x^3)/(3)+2x^2-6x+4`

We have to find the value of x for which function is minimum.

Differentiate w.r.t x

`f'(x)=2x^2+4x-6`

Substitute f'(x)=0

`2x^2+4x-6=0`

`x^2+2x-3=0`

`x^2+3x-x-3=0`

`x(x+3)-1(x+3)=0`

`(x-1)(x+3)=0`

`x=1,-3`

Again, differentiate w.r.t x

`f''(x)=4x+4`

`f''(1)=4(1)+4=8>0`

`f''(-3)=4(-3)+4=-8<0`

Hence, the function is minimum at x=1