The slope at any point of a curve y = f(x ) is given by (d y/d x)=3x2 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 (d y/d x)=3x2 and it passes through (-1 ,1 ) The equation of the curve is (A) y = x3+2 (B) y=-x3-2 (C) y=3x3+4 (D) y=-x3+2

Tardigrade Admin · Accepted Answer

Given, (dy/dx)=3x2 ⇒ dy=3x2dx On integrating, we get y=(3x3/3)+c ⇒ y=x3+c It passes through (-1 ,1 ) ∴ 1=(-1)3+c ⇒ c=2 ∴ y=x3+2

Q. 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

$y = x^{3} + 2$

$y = - x^{3} - 2$

$y = 3 x^{3} + 4$

$y = - x^{3} + 2$

Given, $\frac{d y}{d x} = 3 x^{2}$
$\Rightarrow d y = 3 x^{2} d x$
On integrating, we get
$y = \frac{3 x ^{3}}{3} + c$
$\Rightarrow y = x^{3} + c$
It passes through $(- 1, 1)$
$∴ 1 = (- 1)^{3} + c$
$\Rightarrow c = 2$
$∴ y = x^{3} + 2$

Q. The slope at any point of a curve y=f(x) is given by dxdy​=3x2 and it passes through (−1,1) The equation of the curve is

y=x3+2

y=−x3−2

y=3x3+4

y=−x3+2