3 math problems

(I need steps, thx)

1. Let f(x)=x^3+6x^2−96x+17.

(a) Use the definition of a derivative or the derivative rules to find
f′(x)=

(b) Use the definition of a derivative or the derivative rules to find
f′′(x)=

(c) On what interval is f increasing (include the endpoints in the interval)?
interval of increasing =

(d) On what interval is f decreasing (include the endpoints in the interval)?
interval of increasing =

(e) On what interval is f concave downward (include the endpoints in the interval)?
interval of increasing =

(f) On what interval is f concave upward (include the endpoints in the interval)?
interval of increasing =

2.Suppose a product's revenue function is given by R(q)=−4q^2+1000q .

Find an expression for the marginal revenue function, simplify it, and record your result in the box below. Be sure to use the proper variable in your answer. (Use the preview button to check your syntax before submitting your answer.)

3.In 1973, Braley and Nelson studied the effect of price increases on school lunch participation in the city of Pittsburgh. The Revenue function for the program was given by:
R(q)=(−0.00381q^2+62.476q)/100
where q is the number of lunches bought and R(q) is dollars of revenue (per day).

A) What is the rate of change for this function between 2000 and 13000 lunches purchased? (Include as many decimal places as is possible.)

Answer:

B) What are the appropriate units for the rate of change?
Dollars
Lunches
Lunches per dollars of revenue
Dollars of revenue per lunch
Answer: MR(q)=__________