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PUNE MCA Exam 2015 Question Paper with answers for online practice

Question : 8 of 59

Marks: +1, -0

the curve

y=x^3 - 6x^2 + 9x + 1

has symmetric rotation about the point;

Solution:

Concept:

A cubic curve is symmetric about its point of inflection (where the second derivative is zero).

Explanation:

Given

y = x^3 - 6x^2 + 9x + 1

First derivative:

y' = 3x^2 - 12x + 9

Second derivative:

y'' = 6x - 12

Set

y'' = 0

6x - 12 = 0 \implies x = 2

Find

y

x=2

y = 2^3 - 6(2^2) + 9(2) + 1 = 8 - 24 + 18 + 1 = 3

Thus the inflection point is

(2,3)

, which is the center of rotational symmetry.

Answer:

C. (2, 3)

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