Derivatives and Graphs Section 12.1 Derivatives and Graphs Copyright ©2011 Pearson Education, Inc. All right reserved.

Increasing (-7,-4) (-2,3) Decreasing (-∞,-7) (-4,-2) (3,∞)

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

f(x) increasing decreasing increasing

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x = 0 is the only critical point

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

12.1 # 9, 19, 21, 30, 35

Copyright ©2011 Pearson Education, Inc. All right reserved. Section 12.2 The Second Derivative Copyright ©2011 Pearson Education, Inc. All right reserved.

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

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

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

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

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

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