1. Derivatives and Graphs
Section 12.1
Derivatives and Graphs
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2. Increasing
(-7,-4)
(-2,3)
Decreasing
(-∞,-7)
(-4,-2)
(3,∞)

3. Positive slope – function is increasing
Negative slope – function is decreasing

6. f(x) increasing decreasing increasing

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12. x = 0 is the only critical point

16. x = -3, 4 are critical points
Now choose test points in the three intervals
(-∞,-3), (-3,4), (4,∞)

18. 12.1 # 9, 19, 21, 30, 35

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Section 12.2
The Second Derivative
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20. Price of a stock in month x is given by f(x)
Derivative f’(x) – when price is incr/decr
Derivative of f’(x) – rate of incr/decr

25. Since both functions are always positive, both functions are increasing for x > 0

26. Stock A is increasing at a decreasing rate
Stock B is increasing at an increasing rate

27. s(t) – position of an object at time t
v(t) = s’(t) – velocity at time t
a(t) = s’’(t) – acceleration at time t

28. t must be positive, therefore the object stops in 7/3 seconds.

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