f(x) = |x| is not differentiable at x = 0 because the left-hand and right-hand derivatives are not equal.

For continuity at x = 1, f(1) = k(1)^2 + 2(1) + 1 = k + 3 must be defined for all k.

f(x) is differentiable for all values of a since it is a polynomial function.

f'(x) = 9x^2 - 12x; f''(x) = 18x - 12. Therefore, f''(1) = 18(1) - 12 = 6.

f'(x) = e^x. Therefore, f'(0) = e^0 = 1.

f'(x) = 2x - 4. Therefore, f'(2) = 2(2) - 4 = 0.

f(x) = 1/x is not continuous at x = 0 because it is undefined at that point.

f(x) is a polynomial function, and polynomial functions are continuous everywhere.

f'(x) = cos(x) - sin(x). Therefore, f'(π/4) = cos(π/4) - sin(π/4) = √2/2 - √2/2 = 0.

The limit of f(x) as x approaches 2 is f(2) = 2^2 = 4.