JEE Advanced 2010 Mathematics question
Let f be a real-valued differentiable function on (the set of all real numbers) such that . If the y-intercept of the tangent at any point P(x, y) on the curve is equal to the cube of the abscissa of P, then the value of is equal to
Answer: 9
Solution
The tangent at is ; putting , its y-intercept is . Given , a linear differential equation with integrating factor . Hence
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