Chapter 5.8, Problem 19ES

True-False Determine whether the statement is true or false. Explain your answer. (Assume that $f$ and $g$ denote continuous functions on an interval $\left[a,b\right]$ and that $f_{\text{ave}}$ and $g_{\text{ave}}$ denote the respective average values of $f$ and $g$ on $\left[a,b\right]$ .)

If $g_{\text{ave}}<f_{\text{ave}}$ , then $g\left(x\right)\le f\left(x\right)$ on $\left[a,b\right]$ .