Tag: maxima and minima

The value of $a$ for which the function $f(x)=a\ \sin x+\dfrac{1}{3}\sin 3x$ has an extremum at $x=\dfrac{\pi}{3}$ is

The function $f\left( x \right)\, = \,\dfrac{x}{2}\, + \,\dfrac{2}{x}\,$ has a local minimum at

If $p$ and $q$ are positive real numbers such that ${p}^{2}+{q}^{2}=1$, then the maximum value of $(p+q)$ is

Let $A = (3,-4), B = (1,2)$ .Let $P = (2k-1,2k+1)$ be  a variable point  such that PA+PB is the minimum. then $k$ is

Let f(x) = tan $(\pi /4-x)/cot 2x(x\neq \pi /4)$. The value which should be assigned to f at $x=\pi /4$. So that it is continuous every where, is

Let x and y be two varibles such that $\displaystyle x> 0$ and $xy=1$. Find the minimum value of $x+y$.

In a GP, first term is $1$. If $4T _2 + 5T _3$ is minimum,then its common ratio is.

Let $<\,a _n\,>$ be an $A.P.$ whose first term is $1\;and\;<\,b _n\,>$ is any $G.P.$ whose first term is $2$. If common difference of $A.P.$ is twice of common ratio of $G.P.$ then minimum value of $(a _1b _1+a _2b _2+1)$ is

If 'x' is real, then maximum value of $\dfrac{3x^2+9x+17}{3x^2+9x+7}$ is - 

Let $f\left( x \right) = {x^2} + ax + b.$ If the maximum and the minimum values of $f(x)$ are $3$ and $2$ respectively for $0 \le x \le 2$, then the possible ordered pair(s) of $(a,b)$ is/are-