Question

Using the graph at right, where is the function increasing/decreasing? Where is the function concave up/down? Does this function have any

maxima or minima? Explain how you know

Answer 1

Step-by-step explanation:

Start by calculating the first derivative of f(x) - use the quotient rule

ddx(f(x))=[ddx(x2)]⋅(x2+3)−x2⋅ddx(x2+3)(x2+3)2

f′=2x⋅(x2+3)−x2⋅2x(x2+3)2

f′=2x3+6x−2x3(x2+3)2=6x(x2+3)2❤