Use the function f ( x ) = x^2 − 4 √ x to answer the following questions. a) where is the curve concave upward or downward. b) locate the point of inflection(if any) c) sketch the graph.

Answer 1

f(x) = x² - 4√x has domain [0, ∞)

f'(x) = 2x - 2x^-1/2

f"(x) = 2 + x^-3/2 = 2 + 1 / x^3/2 = (2x^3/2+ 1) / x^3/2 > 0 for all x > 0.

f is concave up on (0, ∞). There are no inflection points.