The slope at any point of a curve y = f(x) is given `(dy)/(dx) = 3x^(2)` and it passes through (-1,1) . The equation the curve is

Options

A. `y=x^(3)+2`
B. `y=-x^(3)-2`
C. `y=3x^(3)+4`
D. `y=-x^(3)+2`

Answer

a

Explanation

Given , `(dy)/(dx) = 3x^(2) rArr dy = 3x^(2) dx`
On integrating, we get
`y=(3x^(3))/2 +C rArr y = x^(3) +C`
It passes through `(-1,1)` .
` :. 1 = (-1)^(3) +C rArr C=2`
` :. Y = x^(3) + 2`