1. Given f(x) = 5/(x²+ 1 )+ 2, find the local minimum and local maximum values if they exist, then find intervals of increase and decrease.

2. Given f(x) = x³ 3x² 144x 140, find the incflection points and intervals of concavity. 1

3. Given f(x) = 3x² 2x³ , on the interval [5, 1], find the absolute maximum and minimum values, and indicate the x-valus at which they occur.

4. Cutoms Ltd. is constructing and open-top, square-based, rectangular fishing tank that will have a volume of 32ft³ . What dimensions minimize the surface area? What is the minimum surface area?

5. For the Vans store in the Temecula Mall, the weeky profit, in dollars, of selling x shoes is P(x) = 0.006x³ 0.2x² + 900x 1200, and currently 60 shoes are sold weekly. a) What is the current weekly profit? b) How much profit would be lost if the shoe store were able to sell only 59 shoes weekly? c) What is the marginal profit when x = 60? d) Use marginal profit to estimate the weekly profit if sales increase to 61 shoes weekly.

6. Find the equation of the tangent line to the curve x⁴ x² y³ = 12 at the point (2, 1).

7. Differentiate a) f(x) = e^(x-4) and b) h(x) = (5x^2 8x)e^{x^2-4x} .

8. Differentiate a) f(x) = log9 (x) (4^x )⁶ and b) h(x) = (x³ x) (ln(x)).

9. Evaluate a) ( 3/x 4e³x)dx and b) ( 3/x + 2/x⁶ + ³x⁴)dx.

10. Approximate the area under the curve of f(x) = 2x² + 1 over the interval [0, 1] by using 6 rectangles.