If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing is

If the tangent to the curve $$xy + ax + by = 0$$ at (1, 1) is inclined at an angle $${\tan ^{ - 1}}2$$ with X-axis, then

Let $$f(x) = a - {(x - 3)^{8/9}}$$, then maxima of $$f(x)$$ is

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