8. Find f′(x) for the following function. Then find f′(8)​, f′(0)​, and f′(−21). F (x) =

13. The profit in dollars from the sale of x expensive watches is P(x)=0.08x2−3x+5x0.5−4400.

Find the marginal profit when ​(a) x=200​, ​(b) x=1000​, ​(c) x=6000​, and ​(d) x=10,000.

14. Use the product rule to find the derivative.

Use the product rule to find the derivative.

y=​(2x2+5​)(2x−3​)

3. Find the indicated outputs for

​f(x)=2x2−3x.

​(a)​ f(0​)

​(b) ​f(​-1)

​(c) ​f(2​)

4. For the piecewise​ function, find the values ​h (−10​), ​h (4​), ​h (5​), and

​h (6​).

h(x)=

6. The net revenue for a certain car company​ (in billions of​ dollars) between the years 2007 and 2012 is approximated by R(x)=−0.703x3+161.1x2−156.8x+425.8​, where x=7 corresponds to the year 2007.

 What is the revenue in 2009​?  What is the revenue in 2012?

21. Find the equilibrium quantity and equilibrium price for the commodity whose supply and demand functions are given.

​Supply: p=100q   ​ Demand: p=−q2+7,500

The equilibrium quantity is q= at price p=​$.

22. Find the equilibrium quantity and equilibrium price for the commodity whose supply and demand functions are given.

​​Supply: p=q2+20q ​Demand: p=−4q2+10q+8400

 The equilibrium quantity is

q=

​(Round to the nearest whole number as​ needed.)

The equilibrium price is

p=​$

[ Can you break down each step so I can understand where I went wrong please.]

​