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Previous Year Paper

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CAT-2007-Previous Years Paper

Question
16 out of 25
 

A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f (x) = 10?



A –110

B –180

C –105

D – 119

E – 159

Ans. E

Let f(x) = ax2+ bx + c

f attains a maximum at x = 1

f’ (x) = 0

â 2ax + b = 0

â b = 2a

Also max f(x) = 3

â a + b + c = 3

â a – 2a + c = 3

â ca = 3

f(0) = 1, c = 1 and a = – 2

Therefore f(x) = – 2x2+ 4x + 1

F(10) = – 2(100) +4(10) + 1 = –200 +41 = –159

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