3.2.36 a. Find the derivative function f' for the following function f. b. Find an equation of the line tangent to the graph of f at (a,f(a)) for the given value F(x) = 4x² + 12x + 5, a = - 2 a. The derivative function f'(x) = 8x + 12. b. The equation of the tangent line is y = - 4x – 11.

A long year-end status report for work is 153 pages long. You need to print 14 copies for a meeting next week. How much is the paper going to cost for those reports? Paper is sold in reams (500 pages) for $3.14 each.$Give your answer to the nearest cent, only for the paper you use (partial reams are OK)

Determine the number of ways to arrange 20 math textbooks (no duplicates) on a shelf. Please show the steps on how to solve it.

In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach both physics and mathematics. How many teach physics ?

Widget Sales Jesaki Inc. is trying to enter the widget market. The research department established the following price-demand, cost, and revenue functions: p(x) = 60 1.20x Price- demand function Cost function C(x) = 210 + 12x R(x) = xp(x) = x(60 - 1.20x) where x is in thousands of widgets and C(x) and R(x) are in thousands of dollars. The price p(x) is the price in dollars of one widget when the demand is a thousand widgets. All three functions have domain 1 ≤ x ≤ 50. Revenue function

My little sister owes my mom $10 right now, and she gets an allowance of $7 every week. She wants to buy a $15 Toy but she has to pay back my mom first.    Model this story using motion on a number line.