The tangent to the curve given parametrically by x = et cos(t), y = et sin(t) at t = π4 makes which angle with the positive x-axis?

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?