$$ \text { The function } y=\tan x-x \text { is } $$

If $$f(x)=\log x+b x^2+a x, x \neq 0$$ has extreme values (or turning points) at $$x=-1$$ and $$x=2$$ then the values of $$\mathrm{a}$$ and $$\mathrm{b}$$ are

The dimensions of the largest rectangle of side $$x$$ and $$y$$ that can be inscribed in the right angled triangle of sides $$\mathrm{a}$$ and $$\mathrm{b}$$ is

If $$(x-a)^2+(y-b)^2=c^2$$, where $$\mathrm{a}, \mathrm{b}, \mathrm{c}$$ are some constants, $$c>0$$ then $$\frac{\left[1+\left(\frac{d y}{d x}\right)^2\right]^{\frac{3}{2}}}{\frac{d^2 y}{d x^2}}$$ is independent of