Academic Detention #2 /yawn

Non-Calculator AP exam Questions 15 and 24

Question 15

Using the Table, estimate f'(2.1).

f(2.0)=1.39
f(2.2)=1.73
f(2.4)=2.10
f(2.6)=2.48
f(2.8)=2.88
f(3.0)=3.30

This problem is really easy if you remember what a derivative is, which is a slope. All you need to do for this problem is find the slope of two points nearest to 2.1. After picking the two points, 2.0 and 2.2, you must use the slope formula, which is f(b)-f(a) over b-a or (f(b)-f(a))/(b-a). Using the chart, you plug in f(b)=1.73 and f(a)=1.39, while b=2.2 and a=2.0.

(f(b)-f(a))/(b-a)
(f(2.2)-f(2.0)/(2.2-2.0)
(1.73 - 1.39)/(.2)
(.34)/(.2)

slope= 1.70

Question 24

At what vale of h is the rate of increase of √h twice the rate of increase of h?

First, pick out the important phrase in this question, which is rate of increase. You know that rate of increase deals with the first derivative and √h is twice as much as h in terms of the derivative, so you can create the equation √h=2h. Then you take the derivative and solve for h.

√h=2h
(1/2)(h^(-(1/2)))=2

1. Multiply (√h) over.

(1/2)=2(√h)

2. Divide 2 over.

(1/4)=(√h)

3. Square both sides.

(1/16)=h

So after a few short steps and simple algebra, you found your answer.