Math 151 Exam 3 Review

1. Solve for x. a) b)

c)

2. Find the derivative of each function.

a) b)

c) d)

e) f) Find y'.

g) ln|sec x| h)

3. When making chocolate fudge, the chocolate mixture must be heated to 234 degrees Fahrenheit and subsequently cooled to 110 degrees F. If the cooling takes 30 min in a room with constant temperature 70 degrees F, what is the temperature t minutes after the mixture is removed from the heat?

4. a) At what interest rate, compounded continuously, will $1500 grow to $2000 in 4 years?

b) A culture grows from 12 grams to 60 grams in 4 hours. Find the weight after t hours.

5. Find y'(x) and express it explicitly.

a) sin y = x b) tan y = x

6. Simplify each expression.

a) cos( arctan 4/5 ) b) sin( 2arccos(1/3)) c) cos( 2arccos(3/4))

d) sec(arctan x ) e)

7. Find the derivative of each function.

a) y = xarctan x Find y'(1).

b) arcsin()

8. Evaluate each limit.

a) b) c)

d) e)

f) g)

9. If the function f(x) has a local max of 4 at x=2 and f(3)=7, what can you say about f' on the interval [2, 3]?

10. Find c in [0, 2] so the conclusion of the Mean Value Theorem holds for .

11. Find the absolute max and min of on the given interval:

a) [-5, 7] b) [0, 4] c) [-3, 0]

12. For , find the inflection point of f and graph f and f'.

13. , f(x) has horizontal asymptotes y=C as x approaches infinity and y= -C as x approaches minus infinity where C is a positive constant, and f(0)=0. Graph f(x).

14. The distance a car has traveled after t hours is given by .

Find the time at which the velocity of the car is greatest and find the max velocity.

15. A right circular cylinder at time t=0 minutes has a radius of 20 cm and a height of 30 cm. The radius is increasing at the constant rate of 2 cm/min. The height is decreasing at the constant rate of 3 cm/min. When will the volume be greatest? Show this is a max and not a min.volume.

16. Given the table of values for f' and f", determine what the 2nd derivative test says about f(x) for each x-value.

x 1 2 3 4

f'(x) 2 0 0 0

f"(x) -7 1 0 -1

17. Sketch a graph of each function.

a)

b)