Let f : R → R be a twice differentiable function such that f(x)m2 - 2m · f'(x) + f''(x) = 0 has equal roots for all x ∈ R. If f(0) = 1, f'(0) = 2, and f(ln x - x) is increasing in the interval (α, β], then find the value of (α + β).

The function f(x) = (x + 1)(x - 2)2 has a local minimum at x equal to:

The slope of the normal to the curve y = xx+2 at x = 1 is:

Given that the radius of a circle is increasing at a constant rate of 1 cm/s, what is the instantaneous rate at which the circle's area is increasing when the radius measures 5 cm?