Lise vs. Steve

Calculus Level 2

Lise jogs along the curve defined by \(f(x) =\dfrac{2(x - 1)^{\frac{3}{2}}}{3}\) from \((1, f(1))\) to \((4, f(4)).\) Steve jogs along the straight line connecting those two points. Steve and Lise both start from \(x = 1\) at the same time and Lise jogs at a speed of \(\frac{7}{\sqrt{3}} \mbox{ units}\mbox{/s}\). What is the speed at which Steve must run (in \(\mbox{ units}\mbox{/s}\)) so that he arrives at \((4, f(4))\) at the same time as Lise?

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