Prove that if f (0) = g(0) and f' (x) ≤ g' (x) for x ≥ 0, then f (x) ≤ g(x) for all x ≥ 0. Hint: Show that the function given by y = f (x) − g(x) is nonincreasing.

Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.

Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval -,x1 and decreases on the interval x1,, then fx1 is a local minimum value.

Let f(x) and g(x) be functions whose graphs are shown below. Which of the following statements is/are true? I. If h(x) = f(x)+ g(x), then h'(2) is negative. II. If h(x) = f(x)g(x), then h'(2) = 0. f(x) III. If h(x) = g(x)' then h'(2) is positive. 6xy f(x) شا 5 4 3 2 1 A. I only B. III only C. II and III only 9(x) 1 2 3 4 5 6 7 MacBook Pro 2x8