# Recent questions tagged maxima-minima

1
What is the maximum value of the function $f(x) = 2x^{2} – 2x + 6$ in the interval $[0,2]?$ $6$ $10$ $12$ $5,5$
2
The greatest and the least value of $f(x)=x^4-8x^3+22x^2-24x+1$ in $[0,2]$ are $0,8$ $0,-8$ $1,8$ $1,-8$
3
Maxima and minimum of the function $f(x)=2x^3-15x^2+36x+10$ occur; respectively at $x=3$ and $x=2$ $x=1$ and $x=3$ $x=2$ and $x=3$ $x=3$ and $x=4$
4
The minimum value of $\mid x^2-5x+2\mid$ is $-5$ $0$ $-1$ $-2$
5
Consider the function $f(x)=\sin(x)$ in the interval $\bigg [​\dfrac{ \pi}{4},\dfrac{7\pi}{4}\bigg ]$. The number and location(s) of the minima of this function are: One, at $\dfrac{\pi}{2} \\$ One, at $\dfrac{3\pi}{2} \\$ Two, at $\dfrac{\pi}{2}$ and $\dfrac{3\pi}{2} \\$ Two, at $\dfrac{\pi}{4}$ and $\dfrac{3\pi}{2}$
6
Consider the functions $e^{-x}$ $x^{2}-\sin x$ $\sqrt{x^{3}+1}$ Which of the above functions is/are increasing everywhere in $[ 0,1]$? Ⅲ only Ⅱ only Ⅱ and Ⅲ only Ⅰ and Ⅲ only
7
Consider a function $f:[0,1]\rightarrow [0,1]$ which is twice differentiable in $(0,1).$ Suppose it has exactly one global maximum and exactly one global minimum inside $(0,1)$. What can you say about the behaviour of the first derivative $f'$ and and second derivative $f''$ ... $f'$ is zero at at least two points, $f''$ is zero at at least two points
8
It is given that $e^a+e^b=10$ where $a$ and $b$ are real. Then the maximum value of $(e^a+e^b+e^{a+b}+1)$ is $36$ $\infty$ $25$ $21$
1 vote
9
Suppose that the function $h(x)$ is defined as $h(x)=g(f(x))$ where $g(x)$ is monotone increasing, $f(x)$ is concave, and $g’’(x)$ and $f’’(x)$ exist for all $x$. Then $h(x)$ is always concave always convex not necessarily concave None of these
1 vote
10
The function $f(x) = x^{1/x}, \: x \neq 0$ has a minimum at $x=e$; a maximum at $x=e$; neither a maximum nor a minimum at $x=e$; None of the above
11
Let $f(x)=\sin x^2, \: x \in \mathbb{R}$. Then $f$ has no local minima $f$ has no local maxima $f$ has local minima at $x=0$ and $x=\pm\sqrt{(k+\frac{1}{2} ) \pi}$ for odd integers $k$ and local maxima at $x=\pm\sqrt{(k+\frac{1}{2} ) \pi}$ for even integers $k$ None of the above
12
The function $f(x)=\sin x(1+ \cos x)$ which is defined for all real values of $x$ has a maximum at $x= \pi /3$ has a maximum at $x= \pi$ has a minimum at $x= \pi /3$ has neither a maximum nor a minimum at $x=\pi/3$
13
The maximum value of the real valued function $f(x)=\cos x + \sin x$ is $2$ $1$ $0$ $\sqrt{2}$
1 vote
14
The function $f(x)$ defined as $f(x)=x^3-6x^2+24x$, where $x$ is real, is strictly increasing strictly decreasing increasing in $(- \infty, 0)$ and decreasing in $(0, \infty)$ decreasing in $(- \infty, 0)$ and increasing in $(0, \infty)$
Consider the function $f(x)=\max(7-x,x+3).$ In which range does $f$ take its minimum value$?$ $-6\leq x<-2$ $-2\leq x<2$ $2\leq x<6$ $6\leq x<10$
Consider the function $f(x)=\bigg(1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\dots+\frac{x^n}{n!}\bigg)e^{-x}$, where $n\geq4$ is a positive integer. Which of the following statements is correct? $f$ has no local maximum For every $n$, $f$ has a local maximum at $x = 0$ $f$ ... maximum at $x = 0$ when $n$ is even $f$ has no local extremum if $n$ is even and has a local maximum at $x = 0$ when $n$ is odd.