The approximate value of $$f(5.001)$$, where $$f(x)=x^3-7x^2+15$$ is

Find the maximum value of $$f(x) = {1 \over {4{x^2} + 2x + 1}}$$.

The point on the curve $$y^2=x$$, the tangent at which makes an angle 45$$^\circ$$ with X-axis is

The length of the subtangent to the curve $${x^2}{y^2} = {a^4}$$ at $$( - a,a)$$ is