Related Rates

Related Rates - Finding Extrema


Eugene is located at (12,0)(-12,0) and walking east at a rate of 3/sec.3\text{/sec}. Elizabeth is located at (0,5)(0,-5) and walking north at a rate of 5/sec.5\text{/sec}. What is the largest speed at which they are walking towards each other?

If the relation between x x and y y is given by 2x+8y=10, 2 x + 8 y = 10, what is the maximum value of 3xy? 3 xy ?

If the surface area of a cylinder is 294π, 294 \pi, what is the largest possible volume of the cylinder?

Consider all ordered pairs of real numbers (x,y) (x,y) which satisfy x2+y24=1x^2 + \frac{y^2}{4} = 1. What is the maximum value of 8x+152y8x + \frac{15}{2}y?

Devin is pumping air into a spherical balloon. If the radius of the balloon is given by r(t)=6t2+23t, r(t) = -6 t^2 + 23t, what is the time t t when the volume of the balloon is maximized?


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