Most Important Selected Qs for JEE AdvancedMathematicsApplication of Derivatives

If f(x) is differentiable function with f^ (0)=1 and 2 x 2 y(f(3 x+3 y)+f(3 x-3 y))= 2 x 2 y(f(3 x+3 y)-f(3 x-3 y)) for all x, b R , then the equation of tangent to y=f(x) at x= 2 is

Options

A2 x+4 y=3 3 -
B2 x-4 y= -3 3
C2 x-y=3 3 -
Dnone of these

Correct answer

B. 2 x-4 y= -3 3

Step-by-step solution

aligned & f(3 x+3 y) (2 x+3 y) = f(3 x-3 y) (2 x-2 y) x, y R & f(x)=k ( 2 x 3 ) & f^ (0)= 2 3 k=1 k= 3 2 & f(x)= 3 2 ( 2 x 3 ) f^ ( 2 )= 3 3 4 aligned Equation of tangent is y- 3 3 4 = 1 2 (x- 2 )

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