Recent questions tagged maxima-minima

The minimum value of $f(x)=\ln \left(1+\exp \left(x^{2}-3 x+2\right)\right)$ for $x \geq 0$, where $\ln (\cdot)$ denotes the natural logarithm, is$\ln \left(1+e^{-1 / 4}\...

Let $f(x, y)$ be a function in two variables $x, y$. Then which of the following is true$\max _{x} \min _{y} f(x, y) \leq \min _{y} \max _{x} f(x, y)$.$\max _{x} \min _{y...

For $x \in[0, \pi / 2], \alpha$ for which $\sin (x) \geq x-\alpha x^{3}$ is$\alpha>1 /(2 \pi)$$\alpha \geq 1 / 6$$\alpha \leq 1 /(2 \pi)$$\alpha=1 / 4$None of the above

Evaluate the value of\[\max \left(x^{2}+(1-y)^{2}\right),\]where the maximisation above is over $x$ and $y$ such that $0 \leq x \leq y \leq 1$.$0$$2$$1 / 2$$1 / 4$$1$

Consider a degree-$5$ polynomial function $f:(-\infty, \infty) \rightarrow(-\infty, \infty)$. If $f$ exhibits at least four local maxima, which of the following is necess...

Calculate the minimum value attained by the function\[\sin (\pi x)-\sqrt{2} \pi x^{2}\]for values of $x$ which lie in the interval $[0,1]$.$\frac{1}{\sqrt{2}}\left(1-\fra...

Consider the positive integer sequence\[x_{n}=n^{50} e^{-(\log (n))^{3 / 2}}, \quad n=1,2,3, \ldots\]Which of the following statements is $\text{TRUE?}$For every $M>0$, t...

If $e^{y}=x^{\frac{1}{x}}$, then $y$ has amaximum at $x=e$minimum at $x=e$maximum at $x=e^{-1}$minimum at $x=e^{-1}$

For a right angled triangle, if the sum of the lengths of the hypotenuse and a side is kept constant, in order to have maximum area of the triangle, the triangle, the ang...

The maximum value of the function $f(x) = \text{ln } (1+x) – x $ (where $x >-1$) occurs at $x=$_______.

The maximum value of $f(x)$= $2x^{3}$ – $9x^{2}$ + $12x – 3$ in the interval $0\leq x\leq 3$ is _______.

For $0 \leq t < \infty ,$ the maximum value of the function $f(t)= e^{-t}-2e^{-2t}$ occurs at$t= log_{e}4$$t= log_{e}2$$t= 0$$t= log_{e}8$

The maximum value of $f(x)=x^3-9x^2+24x+5$ in the interval $[1,6]$ is$21$$25$$41$$46$