REVIEW FOR FINAL EXAM TOMORROW!!!!!!! QUICK HELP PLS

[roswell]

Hey, i really need help with this soon, a few problems on my Math final exam i do not know how to do:
1. Find d²y/dx² for y=(x+2)/(x-3)
2. Let g(x) = -5f(x) and let f'(-7)=6. Find g'(-7)
3. Let f(3) = 0, f'(3)=6, g(3) = 1, and g'(3)= 1/3. Find h'(3) if h(x) = f(x)/g(x)
4. Find dy/dx if x²y + y² = x
5. Find an equation of the tangent line to the graph of x²+2y² = 3 at the point (1,1)
6. A machine is rolling a metal cylinder under pressure. The radius of the cylinder is decreasing at a constant rate of 0.05 inches per second and the volume V is 128pi cubic inches. At what rate is the length h changing when the radius r is 2.5 inches? hint: V=pi*r²h

 

[stapel]

1) Apply the Quotient Rule to "y" to find dy/dx. Apply the Quotient Rule to "dy/dx" to find d²y/dx².

2) Let h(x) = -5, so g(x) = h(x)f(x). Apply the Product Rule. Then plug in the given values.

3) Apply the Quotient Rule, and then plug in the given values.

4) Use implicit differentiation and then solve the result for "dy/dx =". Or else rearrange the equation as "y² + x²y - x = 0" and apply the Quadratic Formula to solve explicitly for "y"; then differentiate. (The first way would probably be easier, though.)

5) Differentiate implicitly. Evaluate the derivative equation at x = 1, y = 1, and solve for "dy/dx", as this, naturally, is the value of the slope m at (x, y) = (1, 1). Then take the point and the slope and plug them into the point-slope form (or whatever other formula you prefer to use) to find the tangent-line equation.

6) You know the volume formula for a cylinder: V = (pi)r²h. You are given that dr/dt = -0.05 and that V is fixed at 128(pi), so dV/dt = 0.

Use the volume formula and the given volume value to solve for h in terms of r. Then differentiate the original volume formula implicitly with respect to time "t". Plug in the given values for r, dr/dt, and dV/dt. Use the substitution to allow for solving for "dh/dt".

If you get stuck, please reply showing all your steps. Thank you.

Eliz.