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# The Minimum Value of the Function F ( X ) = 2 X 3 − 21 X 2 + 36 X − 20 is - CBSE (Science) Class 12 - Mathematics

#### Question

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

• -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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Solution 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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