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151 WebCalc Fall 2002-copyright Joe Kahlig
In Class Questions
MATH 151-Fall 02
November 12
1. Here is the graph of f 0 (x). The domain is given and it is all real numbers. Where is f (x)
increasing? decreasing? What are the critical values of f (x).
E
A
B
C
D
2. Find where the function is increasing and decreasing and classify the critical values.
√
(a) y = 3 x2 − x
(b) y = x ln x
3. If y 0 and the domain are given below, find where the function is increasing and decreasing and
classify the critical values.
2
(a) y 0 = x(x2 − 25)(x − 10)4 ex −9 and the domain is all real numbers.
−3x + 7
(b) y 0 =
and the domain is all real numbers except x = −5.
(x + 5)3
4. Find the absolute maximum and absolute minimum for the function on the given intervals.
(a) y = x3 − 12x on [−3, 5]
(b) y = x12 on [−2, 4]
(c) y = x12 on [2, 4]
(d) y = cos(x) on
−π 3π
2 , 2
5. For the function, f (x) = x1 , there is no number,c, in the interval [−2, 2] such that f 0 (c) = .25.
Why doesn’t this violate the mean value theorem?
6. A toll road is 100miles long. You clock into the road at 8am and at 9:15 you exit the road. If
the maximum speed allowed on the road is 70mph, do you get a ticket?
7. Suppose the f 0 (x) ≤ 2 on the interval [−3, 10] and f (1) = 1.5. What is the maximum value of
f (6)?