#1 through #9: Find the derivative of each expression. Use correct notation for each derivative! Algebraic simplification of your result is not required.

1) f(x) = - 100x^1.25 - 10x^-0.7+ 8250

2) f(x) = ln (7.5x² - 11x + 37.5)

3) f(t) = e (-1.4t³+ ln2.45 + 6.98t)

4) f(x) = log₆ (5x^2.5 - 7x)

5) y = (2.085t ² - 72.5t +2.75e)^1.625

6) f(x) = (x^2.4 - 2.6lne ) (10x^1.3 - e^-X )

7) f(w) = 13^{(1.6W3 - 3.2W)}

8) f(x) = 1.74 e^X - 4e^-x / 12.98 x² + e^1.05

9) y = 5 ln w + ln 4 + ³

10) Find the following Antiderivative and simplify. Check your result. { (40x³ - 12x^0.5 + e^x ) dx

11) Find the following Antiderivative and simplify. Check your result. { (4.8x^-5+ 14x -3/x ) dx

12) What interest rate is needed for a deposit of $8000 to grow to $15,000 in 90 months, assuming that interest is compounded continuously? Solve to 8 decimal places. (Remember there are 12 months in a year.)

13) For each function below: find the Domain of the function; use correct notation. Then find the indicated Limit using computational approach. Show your work! Be precise. a) lim 12x + 72

x-->6⁺ X² - 36

b) lim 8x- 24

x -->3 x² - 10x + 21

14) An office supply store sells a four-drawer oak file cabinet. A consultant has determined the following price-demand relation, where "x" is monthly demand and selling price is "p" (in dollars). The price-demand relation is given by: x = 36 ln 540 - 48 ln p

a) For the oak file cabinet described above, find and simplify the expression for Elasticity of Demand:

Now evaluate the Elasticity of Demand for each selling price below. Classify the type of Elasticity found, and describe the Impact on Revenue of a price increase in the neighborhood of the given price point.

b) Selling price is $250.00 (Use 4 decimal places to evaluate the Elasticity of Demand.)

c) Selling price is $400.00 (Use 4 decimal places to evaluate the Elasticity of Demand.)

d) Selling price is $304.50 (Use 4 decimal places to evaluate the Elasticity of Demand.)

15) A small family-owned business in Vermont has introduced a new toy that has price-demand relation: p = 60 x - where "p" is price in dollars and "x" is demand per week The total weekly Cost of producing this new toy is given by: C(x) = 0.40x + 800

a) Find the Revenue function for this new toy. Simplify the function.

b) Find the Profit function for this new toy. Simplify the function.

c) Find the expression for Marginal Revenue.

d) Find the incremental Revenue associated with the 3250^th toy that is produced and sold next week. Solve to 3 decimal places.

e) Find the expression for Marginal Profit.

f) Find the incremental Profit associated with the 6725^th toy that is produced and sold next week. Solve to 3 decimal places.

16) A shop in Greenport sells "x" bottles of olive oil per week. The shop's total Profit per week is given by: P(x) = 198x^1/2 - 8x - 625 where "x" is number of bottles of olive oil sold per week

a) How many bottles of olive oil (x) should be sold each week to Optimize the shop's total Profit per week? Use the Optimization procedure based on the Second Derivative Test. Show Work below!

b) What is the shop's total Profit per week at the optimal value of "x" that you found above? (Solve for Profit to the nearest penny.)