The function $f(x)=\sin^4(x)+\cos^4(x)$, on interval $\left(0,\dfrac{\pi}{2}\right)$, has

$f(x)=\sin x+\frac{1}{2} \cos 2 x \text { in }\left[0, \frac{\pi}{2}\right]$

(A) $f^{\prime}(x)=\cos x-\sin 2 x$

(B) The critical points of the function are $x=\frac{\pi}{6}$ and $x=\frac{\pi}{2}$

(C) The minimum value of the function is $2$

(D) The maximum value of the function is $\frac{3}{4}$

Choose the correct answer from the options given below :

The rate of change of $\sqrt{x^2-2}$ with respect to $\dfrac{x}{x+1}$ at $x=2$ is :

Based on above information answer the following question :

If area of the flower bed is maximum, then area (in $m^2$) of the garden, which is outside the flower bed is :

The real valued function $f(x) = 12x^\frac{4}{3} - 6x^\frac{1}{3}, x \in [-8, 8]$ has absolute maximum value equal to

The slope of normal to the curve $y = 3x^2 + 3 \sin 3x$, at $x = 0$ is:

The interval in which the function $f(x)=x^3-12x^2+36x+20$ is increasing, is