Let a function g : [0, 4] → R be defined as g(x) = max0≤t≤x {t3 - 6t2 + 9t - 3} for 0 ≤ x ≤ 3, and g(x) = 4 - x for 3 < x ≤ 4. Then the number of points in the interval (0, 4) where g(x) is NOT differentiable is:

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?