Question

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

• A. $y = x^{3}+2$
• B. $y=-x^{3}-2$
• C. $y=3x^{3}+4$
• D. $y=-x^{3}+2$

Answer 1

Answer: (A)

$y = x^{3}+2$

Answer 2

Given, $\frac{dy}{dx}=3x^{2}$
$\Rightarrow dy=3x^{2}dx$
On integrating, we get
$y=\frac{3x^{3}}{3}+c$
$\Rightarrow y=x^{3}+c$
It passes through $(-1 ,1 )$
$\therefore 1=\left(-1\right)^{3}+c$
$\Rightarrow c=2$
$\therefore y=x^{3}+2$