If a quadratic function in $x$ has the value 19 when $x=1$ and has a maximum value 20 when $x=2$, then the function is

If the length of the diagonal of a square is increasing at the rate of $0.1 \mathrm{~cm} / \mathrm{sec}$. What is the rate of increase of its area when the side is $\frac{15}{\sqrt{2}} \mathrm{~cm}$ ?

The function $y=\frac{\log x}{x^3}$ is strictly increasing function for

The curve $4 y=3 x^4-2 x^2$ attains ----------- at the points $x=-\frac{1}{\sqrt{3}}$ and $x=\frac{1}{\sqrt{3}}$