The minimum value of the function f(x)=2x^3-21x^2+36x-20 is ______________ .

Question

KollegeApply · Accepted Answer

-128 Given:- f(x)=2x^3-21x^2+36x-20 rArrf'(x)=6x^2-42x+36 For a local maxima or a local minima, we must have f'(x)=0 rArr6x^2-42x+36=0 rArrx^2-7x+6=0 rArr(x-1)(x-6)=0 rArrx=1, 6 Now, f''(x)=12x-42 rArrf''(1)=12-42=-30<0 So, x = 1 is a local maxima. Also, f''(6)=72-42=30>0 So, x = 6 is a local minima. The local minimum value is given by `f(6)=2(6)^3-21(6)^2+36(6)-20=-128`

AChoose Your Answer