Monotonicity

The value of $c$ for the function $f(x)=x^{2},x\in[-1,1]$ satisfied the Rolle's theorem is

A wire of length 64 m is to be bent to form a rectangle such that its area is maximum, then its area is.....

The value of $c$ for the function $f(x)=x^{2}-4x+10$ on $[0,4]$ satisfied the Rolle's theorem is

If the function $x^{4}-62x^{2}+ax+9$ attains its local maximum value at $x=1$ then the value of $a$ is

A ball is thrown in the air. Its height at any time $t$ is given by $h=3+14 t-5 t^{2}$, then the maximum height it can reach

The function $f(x)=x^{3}-3x^{2}+3x-100,x\in R$ is

The local maximum value of $f(x)=\dfrac{1}{\left( x^{2}+2 \right)}$ is

The approximate value of $x^{3}-2x^{2}+3x+2$ at $x=2.01$ is

Find the equations of tangent and normal to the curve $y=3x^{2}-x+1$ at $P(1,3)$.

The maximum value of the function $f(x)=\sin x+\cos x$ in $\left( 0,\dfrac{\pi}{2} \right)$ is

Find the interval of increase of the function $f(x)=\dfrac{\log x}{x}$.

Find the interval on which the function $f(x)=(x+1)^{3}(x-3)^{3}$ is decreasing

$\sqrt{144.02}$

A spherical balloon is expanding. If the radius is increasing at the rate of 2 cm/mm the rate at which the volume increases (in cubic centimeters per minute) when the radius is 5 cm, is

The sum of two nonzero numbers is 4 . The minimum value of the sum of their reciprocals is