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JEE Advanced Mathematics question

MathematicsApplication of DerivativesJEE Advanced

Let be a real-valued differentiable function on , the set of real numbers, such that . If the -intercept of the tangent at any point on the curve is equal to the cube of the abscissa of then the value of is equal to

Answer: 9

Solution

Tangent at : . Putting , the -intercept is . So

y - x = ⇒ - Missing argument for \frac\frac yx = -.

Integrating factor : $(Missing argument for \frac\frac

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Question ID VK-110785