Question
The function ${x^5} - 5{x^4} + 5{x^3} - 10$  has a maximum, when $x =$

Answer

c
(c) Obviously, it has a maximum at $x = 1$.

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

Similar questions

Let the solution curve $y=y(x)$ of the differential equation $\left(4+x^{2}\right) d y-2 x\left(x^{2}+3 y+4\right) d x=0$ pass through the origin. Then $y(2)$ is equal to
The angle of intersection between the curves ${x^2} = 4(y + 1)$ and ${x^2} = - 4(y + 1)$ is
If $x^2-y^2+2 h x y+2 g x+2 f y+c=0$ is the locus of a point, which moves such that it is always equidistant from the lines $x+2 y+7=0$ and $2 x-y$ $+8=0$, then the value of $\mathrm{g}+\mathrm{c}+\mathrm{h}-\mathrm{f}$ equals
If $a,\;b,\;c$ are in $G.P.$ and $x,\,y$ are the arithmetic means between $a,\;b$ and $b,\;c$ respectively, then $\frac{a}{x} + \frac{c}{y}$ is equal to
If for $x \geq 0, y=y(x)$ is the solution of the differential equation $(\mathrm{x}+1) \mathrm{d} \mathrm{y}=\left((\mathrm{x}+1)^{2}+\mathrm{y}-3\right) \mathrm{d} \mathrm{x}, \mathrm{y}(2)=0$ then $y(3)$ is equal to
Consider the function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined by

$f(x)=\frac{2 x}{\sqrt{1+9 x^2}}$. If the composition of $f, \underbrace{(f \circ f \circ f \circ \ldots \circ f)}_{10 \text { times }}(x)=\frac{2^{10} x}{\sqrt{1+9 \alpha x^2}}$, then the value of $\sqrt{3 \alpha+1}$ is equal to....................

Let $X$ have a binomial distribution $B ( n , p )$ such that the sum and the product of the mean and variance of $X$ are $24$ and $128$ respectively. If $P ( X > n -3)=\frac{ k }{2^{ n }}$, then $k$ is equal to.
Let $a, b, c, d$ be real numbers such that $\sum \limits_{k=1}^n\left(a k^3+b k^2+c k+d\right)=n^4$, for every natural number $n$. Then, $|a|+|b|+|c|+|d|$ is equal to
The number of real solutions of the equation

$\sin ^{-1}\left(\sum_{i=1}^{\infty} x^{i+1}-x \sum_{i=1}^{\infty}\left(\frac{x}{2}\right)^i\right)=\frac{\pi}{2}-\cos ^{-1}\left(\sum_{i=1}^{\infty}\left(-\frac{x}{2}\right)^i-\sum_{i=1}^{\infty}(-x)^i\right)$

lying in the interval $\left(-\frac{1}{2}, \frac{1}{2}\right)$ is. . . . .

(Here, the inverse trigonometric functions $\sin ^{-1} x$ and $\cos ^{-1} x$ assume values in $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ and $[0, \pi]$, respectively.)

The number of common tangents to the circles ${x^2} + {y^2} - 4x - 6y - 12 = 0$ and ${x^2} + {y^2} + 6x + 18y + 26 = 0$ is