Problem 51E

51. (a) If $f(x)=x \sqrt{5-x}$, find $f^{\prime}(x)$.

(b) Find equations of the tangent lines to the curve $y=x \sqrt{5-x}$ at the points $(1,2)$ and $(4,4)$.

(c) Illustrate part (b) by graphing the curve and tangent lines on the same screen.

(d) Check to see that your answer to part (a) is reasonable by comparing the graphs of $f$ and $f^{\prime}$.

Step-by-Step Solution