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Most Important Selected Qs for JEE AdvancedMathematicsApplication of Derivatives

Given two curves : y =f( x ) passing through (0,1) and y = _ - ^ x f( t ) dt passing through (0, 1 3 ) . The tangents drawn to both the curves at the points with equal abscissas intersects on x -axis. Find the value of n f(3) .

Correct answer

9

Step-by-step solution

Equation the tangent to the curve y =f( x ) is ( Y - y )=f^ ( x )( X - x ) equation of the tangent to the curve y ₁= g ( x )= ^ x f( t ) dt is aligned & ( Y - y ₁ )= g ^ ( x )( X - x ) & ( Y - y ₁ )=f( x )( X - x ) aligned Given that tangent with equation abscissa intersects on x -axis x- y f^ (x) =x- y₁ f(x) aligned f(x) f^ (x) & = y₁ f(x) f(x) y₁ & = f^ (x) f(x) g^ (x) g(x) & = f^ (x) f(x) aligned Integrating both sides we get, ng ( x )= f( x )+ c aligned & n ( g ( x ) f( x ) )= c g ( x )= k f( x ) & g (0)= k f(0

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