Math 115-01 – Fall 2008 – HW #31 problems
These problems are due Wed, Nov 19.
Section 4.9:
In Exercises 2, 4, 6, 8, and 12, find the most general antiderivative of the given function. (Check your answer by
differentiation.)
2. f ( x) = 1 − x 3 + 12 x 5
4. f ( x) = 2 x + 3 x1.7
6. f ( x) = 4 x 3 + 3 x 4
8. g ( x) =
5 − 4 x3 + 2 x 6
x6
12. f ( x) =
x2 + x + 1
x
14. Find the antiderivative F of the function f ( x) = 4 − 3(1 + x 2 ) −1 that satisfies the condition F (1) = 0 . Check
your answer by comparing the graphs of f and F.
16. If f ′′( x) = 2 + x 3 + x 6 , find f. [Note: Your solution will involve two arbitrary constants.]
30. Find a function f such that f ′( x) = x 3 and the line x + y = 0 is tangent to the graph of f.
47. A stone was dropped off a cliff and hit the ground with a speed of 120 ft/sec. What is the height of the cliff.
[Note: The acceleration due to gravity is 32 ft/sec2 downward.]
50. A car braked with constant deceleration of 16 ft/sec2, producing skid marks measuring 200 ft before coming
to a stop. How fast was the car traveling when the brakes were first applied?