Q. 765.0( 1 Vote )

# Choose the correct answer out of 4 options given against each Question

If f(x) = 1 – x + x^{2} – x^{3} … –x^{99} + x^{100}, then f’(1) is equal to

A. 150

B. –50

C. –150

D. 50

Answer :

f(x) = 1 – x + x^{2} – x^{3} + …….- x^{99} + x^{100}

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

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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