The slope at any point of a curve $ y=f(x) $ is given by $ \frac{d y}{d x}=3 x^{2} $ and it passes through $ (-1,1) $ The equation of the curve is

Question

The slope at any point of a curve $ y=f(x) $ is given by $ \frac{d y}{d x}=3 x^{2} $ and it passes through $ (-1,1) $ The equation of the curve is, $ y=x^{3}+2 $, $ y=-x^{3}-2 $, $ y=3 x^{3}+4 $, $ y=-x^{3}+2 $

MARKS App · Accepted Answer

We have, d y d x = 3 x 2 ⇒ d y = 3 x 2 d x Integrating both sides, we have ∫ d y = 3 ∫ x 2 d x ⇒ y = 3 x 3 3 + c ⇒ y = x 3 + c It is passing through - 1 , 1 . Therefore, ⇒ 1 = - 1 3 + c ⇒ c = 2 Hence, the required curve is y = x 3 + 2

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