Q. 765.0( 1 Vote )

# Choose the correct answer out of 4 options given against each QuestionIf f(x) = 1 – x + x2 – x3 … –x99 + x100, then f’(1) is equal toA. 150B. –50C. –150D. 50

f(x) = 1 – x + x2 – x3 + …….- x99 + x100

f’(x) = -1 + 2x – 3x2 + ……. – 99x98 + 100x99

f’(1) = -1 + 2(1) – 3(1)2 + ……. – 99(1)98 + 100(1)99

= (-1 – 3 – 5…… -99) + (2 + 4 + 6 +….. + 100)
=

[Using Arithmetic Progression, where d = -2 & 2, a = -1 & 2 & n = 50 respectively]

= 25 (-2 – 98) + 25 (4 + 98)

= 25 (-100) + 25 (102)

= 25 (-100 + 102)

= 25 (2)

= 50

Hence Option (D) is the correct answer.

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