If x=2−31, find the value of x3−2x2−7x+5.

Given f:R→R, f(x)=(x−1)(x−2)2f′(x)=(x−2)2+2(x−1)(x−2)=(x−2)(x−2+2x−2)=(x−2)(3x−4)f(x) is strictly increasing if f′(x)>0(x−2)(3x−4)>0x2f(x) is strictly decreasing if f′(x)<0(x−2)(3x−4)<034<x<2

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If x={1}{2-{3}}, find the value of x^3-2x^2-7x+5.

Question

If $x = \frac{1}{2 - 3}$ , find the value of $x^{3} - 2 x^{2} - 7 x + 5$ .

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Amelia Discussed

x = \frac{1}{2 - 3}

, find the value of

x^{3} - 2 x^{2} - 7 x + 5

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

Given

f : R \to R

f (x) = (x - 1) (x - 2)^{2}

f^{'} (x) = (x - 2)^{2} + 2 (x - 1) (x - 2)

= (x - 2) (x - 2 + 2 x - 2)

= (x - 2) (3 x - 4)

f (x)

is strictly increasing if

f^{'} (x) > 0

(x - 2) (3 x - 4) > 0

x < \frac{4}{3}

and

x > 2

f (x)

is strictly decreasing if

f^{'} (x) < 0

(x - 2) (3 x - 4) < 0

\frac{4}{3} < x < 2

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Question Text	If $x = \frac{1}{2 - 3}$ , find the value of $x^{3} - 2 x^{2} - 7 x + 5$ .
Answer Type	Text solution:1
Upvotes	150

If x=2−3​1​, find the value of x3−2x2−7x+5.

Text solutionVerified

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If $x = \frac{1}{2 - 3}$ , find the value of $x^{3} - 2 x^{2} - 7 x + 5$ .