Question

Average rate of change of polynomials f(x)=x^2+10 Over which interval does f have a positive average rate of change?

answers are
[−3,1]
[−1,2]
[−4,−1]
[−3,3]

Answer 1

Explanation:

The answer is [−3,3]. The average rate of change of f(x)=x^2+10 over an interval [a,b] is given by (f(b)-f(a))/(b-a). Since f(x)=x^2+10 is a polynomial of degree two, it is always increasing, and so its average rate of change is always positive. Thus, the average rate of change of f(x) over any interval [a,b] where a<b is positive, so the answer is [−3,3].