Suppose $f(x)=x(x+3)(x-2)$,where $x \in [-1,4]$. Then,a value of $c$ in $(-1,4)$ satisfying $f^{\prime}(c)=10$ is

$y=\log \left\{\left(\frac{1+x}{1-x}\right)^{1 / 4}\right\}-\frac{1}{2} \tan ^{-1}(x)$,then $\frac{d y}{d x}$ is equal to

If $\frac{d}{d x}\left\{\left(\frac{x-1}{x-\sqrt{x}}\right) e^{2 x+1}\right\}=\frac{x-1}{x-\sqrt{x}} e^{2 x+1} f(x)$,then $f(4)=$

Find the derivative of the following function (it is to be understood that $a, b, c, d, p, q, r$ and $s$ are fixed non-zero constants and $m$ and $n$ are integers): $\frac{ax+b}{px^{2}+qx+r}$

Which one of the following is false?

For the function $f(x) = x^2 - 6x + 8$ where $2 \le x \le 4$,the value of $x$ for which $f'(x)$ vanishes is: