The function {f}(x)=2 x³-9 x²+12 x+2 is decreasing in

Correct Answer is : 1<x<21 < x < 21<x<2

Correct Answer is : 1<x<21 < x < 21<x<2

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MHTCET 15 May 2024 Shift 2 Paper

Question : 118 of 150

Marks: +1, -0

The function

\mathrm{f}(x)=2 x^{3}-9 x^{2}+12 x+2

is decreasing in

Solution:

Concept:

A function is decreasing where its derivative is negative.

Explanation:

Given

f(x)=2x^{3}-9x^{2}+12x+2

, find

f'(x)

f'(x)=6x^{2}-18x+12

Factor:

f'(x)=6(x-1)(x-2)

The critical points are

x=1

and

x=2

Test the sign of

f'(x)

in the intervals.

For

x<1

, take

x=0

f'(0)=12>0

For

1 < x<2

, take

x=1.5

f'(1.5)=-1.5<0

For

x>2

, take

x=3

f'(3)=12>0

Thus,

f'(x)<0

only for

1 < x<2

Answer:

The function is decreasing in

1 < x<2

Correct option: A.

1 < x<2

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