Question

If $f^{\prime }\left(x\right)=3x^2+5$ and $f\left(0\right)=-1$ , then $f\left(x\right)=$

• A. $x^3+5x-1$
• B. $x^3+5x+1$
• C. Both (a) and (b)
• D. None

Answer 1

The correct option is A $x^3+5x-1$

Given,

$f^{\prime }\left(x\right)=3x^2+5$

$f\left(x\right)=\int f^{\prime }\left(x\right)dx$

$\int (3x^2+5)dx$

$=3\left(\frac{x^3}{3}\right)+5x+C$

$\therefore f\left(x\right)=x^3+5x+C$

Given $f\left(0\right)=-1$

$0^3+5\left(0\right)+C=-1$

$\therefore C=-1$

$\therefore =x^3+5x-1$