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in Differential equations by (33.0k points)

Let f be a real-valued differentiable function on R (the set of real numbers) such that f(1) = 1. If the y-intercept of the tangent at any point P(x, y) on the curve y = f(x) is equal to the cube of the abscissa of P, the value of f(– 3) is ...

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Best answer

The equation of tangent at any point (x, y) to the curve y = f(x) is 

Y – y = f'(x)(X – x)

Intercept on y-axis is y – xf'(x) 

It is given that, y – xf'(x) = x3

Hence, the solution is

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