If f'(x) = x^2 + 5 and f(0) = - 1, then f(x) = - Vidyadip

MCQ

If $f'(x) = {x^2} + 5$ and $f(0) = - 1$, then $f(x) = $

A
${x^3} + 5x - 1$
B
${x^3} + 5x + 1$
✓
$\frac{1}{3}{x^3} + 5x - 1$
D
$\frac{1}{3}{x^3} + 5x + 1$

✓

Answer

Correct option: C.

$\frac{1}{3}{x^3} + 5x - 1$

c
(c) Given that $f'(x) = {x^2} + 5$ and $f(0) = - 1$
==> $f(x) = \frac{{{x^3}}}{3} + 5x + c$. If $x = 0,$ then $f(0) = c$

==> $c = - 1$.
Hence $f(x) = \frac{{{x^3}}}{3} + 5x - 1.$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The curve represented by $x = 3(\cos t + \sin t)$, $y = 4(\cos t - \sin t)$ is

An orthogonal matrix is

The greatest coefficient in the expansion of ${(1 + x)^{2n + 2}}$ is

If $\int_{}^{} {(\cos x - \sin x)\;dx = \sqrt 2 \sin (x + \alpha ) + c} $, then $\alpha = $

A value of ${\tan ^{ - 1}}\,\,\left( {\sin \,\left( {{{\cos }^{ - 1}}\left( {\sqrt {\frac{2}{3}} } \right)} \right)} \right)$ is

Area of the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ is

If $a,\;b,\;c,\;d$ and $p$ are different real numbers such that $({a^2} + {b^2} + {c^2}){p^2} - 2(ab + bc + cd)p + ({b^2} + {c^2} + {d^2}) \le 0$, then $a,\;b,\;c,\;d$ are in

The general solution of the differential equation $\left(x-y^{2}\right) d x+y\left(5 x+y^{2}\right) d y=0$ is.

Let $\omega $ be a complex number such that $2\omega + 1 = z$ where $z = \sqrt { - 3} $ . If $\left| {\begin{array}{*{20}{c}}1&1&1\\1&{ - {\omega ^2} - 1}&{{\omega ^2}}\\1&{{\omega ^2}}&{{\omega ^7}}\end{array}} \right| = 3k$ then $k$ is equal to :

Suppose $a_{1}, a_{2}, \ldots, a_{ n }, \ldots$ be an arithmetic progression of natural numbers. If the ratio of the sum of the first five terms of the sum of first nine terms of the progression is $5: 17$ and $110< a_{15} < 120$ , then the sum of the first ten terms of the progression is equal to -