Question

If the average rate of change of f(x) with respect to x over the interval [a, b] is m, then find the value of $\frac{1}{m^2}$

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Answer 1

We saw that the average rate change of a function over the interval [a,b] is the slope of the secant connecting the corresponding points on the graph

From the graph we can see that the slope of the secant connecting the corresponding points is 30 degrees. Slope of this line will be equal to $tan\left(30\right)=\frac{1}{\sqrt{3}}$ This is the average rate of change of f(x) over the interval [a, b], which is given as m. So the value $\frac{1}{m^2}=3$