#### Question

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

##### Options

-128

-126

-120

none of these

#### Solution

`-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`

Is there an error in this question or solution?

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The Minimum Value of the Function F ( X ) = 2 X 3 − 21 X 2 + 36 X − 20 is Concept: Graph of Maxima and Minima.

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