A. Use implicit differentiation and differentiate the damned thing, you get

Isolate the dy/dx on one side and you get

B. Plug the x coordinate value back into the original equation. You get two points 1/4 and 2. It's easy to also plug all those values into the dy/dx equation that you just proved is right, and determine which one creates a horizontal line (dy/dx = 0).

= P (3,2)

C. Differentiate your dy/dx equation again and don't forget to plug in your original dy/dx equation into the places where you have dy/dx.

Since you know that at P there is a horizontal line, it is either a relative max or min. So all you have to do is figure out which concavitiy it is.

Plug P into the d©÷y/dx©÷ and you figure out it is -2/7

= Relative Maximum

A. The equation for the problem ends up being

(After multiplying the equation out and then using partial fractions to get the anti-derivative)

Plug in t = 0 and set the equations equal to 3 and 20 respectively.

In addition to this, you need to find each C for each equation.

Then solve respectively.

both equations end up = 12

B. P(t) is growing the fastest when dP/dt is a maximum.

so dP/dt = 0 and d©÷P/dt©÷ = 0

Solve for zero for both equations.

=> P=6

C. You have to use normal antidifferentiation to get Y(t). But first you must plug in the values that were given to you [ Y(0) = 3 ]. Use this value as you antidifferentiate and find c.

c = ln 3

Then remember to eliminate the ln on the y side by raising everything to e.

=

D. Y(t) is increasing on 0 ¡Â t ¡Â 12 and decreasing on t > 12.

Y(t) < 3 = Y(0)

= 0

A. Remember that Taylor form is and that a = 0.

With this information you just plug your stuff in and get =

B.
=

C.
¡Â = < .01

D. To finish off this question you have to realize that

which ends up equaling

=