Page:Calculus Made Easy.pdf/129

 keep always in the same proportion to each other; that is, at any instant, the cylinder is similar to the original cylinder. When the radius of the base is $$r$$ feet, the surface area is increasing at the rate of $$20$$ square inches per second; at what rate is its volume then increasing?

The volume changes at the rate of $$10r$$ cubic inches.

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Exercises IX. (See page 258 for Answers.)

(1) What values of $$x$$ will make $$y$$ a maximum and a minimum, if $$y=\dfrac{x^2}{x+1}$$?

(2) What value of $$x$$ will make $$y$$ a maximum in the equation $$y=\dfrac{x}{a^2+x^2}$$?