JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Hard

1 of 1

Analyzing +4 | -1

Let

f\left( x \right)

be defined on

R

such that

f\left( 1 \right) = 2,f\left( 2 \right) = 8

and

f\left( {u + \upsilon } \right) = f\left( u \right) + ku\upsilon - 2{\upsilon ^2}

for all

u,\upsilon \in R

(

k

is a fixed constant). Then,

View answer and explanation

Correct option: A

f'\left( x \right) = 8x

Option A (

f'(x) = 8x

) is correct because by substituting

u = x

and

\upsilon = h

into the given functional equation and taking the limit as

h

approaches 0, we find the derivative.

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