Question

Describe the x-values at which the function is differentiable. (Enter you answer using interval notation.)

f(x) = (x+2)^2/3

Answer 1

The function f(x) = (x+2)^2/3 is differentiable for all real values of x because it is a rational function and both the numerator and denominator are polynomials, which are continuous and have no discontinuities. Therefore, the interval for x for which the function is differentiable is (-∞,∞). In interval notation, this is expressed as:
(-∞,∞)