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Let {f{{({x})}}}={x}^{{3}}-{3}{({a}-{2})}{x}^{{2}}+{3}{a}{x}+{

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Let $f (x) = x^{3} - 3 (a - 2) x^{2} + 3 a x + 7$ and $f (x)$ is increasing in $(0, 1]$ and decreasing is $[1, 5)$ , then roots of the equation $\frac{f ( x ) - 14}{( x - 1 ) ^{2}} = 0$ is (A) $1$ (B) $3$ (C) $7$ (D) $- 2$

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Samuel Discussed

Let

f (x) = x^{3} - 3 (a - 2) x^{2} + 3 a x + 7

and

f (x)

is increasing in

(0, 1]

and decreasing is

[1, 5)

, then roots of the equation

\frac{f ( x ) - 14}{( x - 1 ) ^{2}} = 0

is (A)

1

(B)

3

(C)

7

(D)

- 2

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Question Text

Let

f (x) = x^{3} - 3 (a - 2) x^{2} + 3 a x + 7

and

f (x)

is increasing in

(0, 1]

and decreasing is

[1, 5)

, then roots of the equation

\frac{f ( x ) - 14}{( x - 1 ) ^{2}} = 0

is (A)

1

(B)

3

(C)

7

(D)

- 2

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