3. f(x) and g(x) are a differentiable function for all reals and h(x) = g[f(2x)]. The table below gives selected values for f(x), g(x), f ‘(x), and g ‘(x). Find the value of h ‘(1).
| x |
1 |
2 |
3 |
4 |
5 |
6 |
| f(x) |
0 |
3 |
2 |
1 |
2 |
0 |
| g(x) |
1 |
3 |
2 |
6 |
5 |
0 |
| f ‘(x) |
3 |
2 |
1 |
4 |
0 |
2 |
| g ‘(x) |
1 |
5 |
4 |
3 |
2 |
0 |
4. The table of values below shows the rate of water consumption in gallons per hour at selected time intervals from t = 0 to t = 12.
Using a Trapezoidal sum with 5 subintervals, estimate the total amount of water consumed in that time interval.
| x |
0 |
2 |
5 |
7 |
11 |
12 |
| f(x) |
5.7 |
5.0 |
2.0 |
1.2 |
0.6 |
0.4 |
5.The function is continuous on the interval [10, 20] with some of its values given in the table above. Estimate the average value of the function with a Left Hand Sum Approximation, using the intervals between those given points.
| x |
10 |
12 |
15 |
19 |
20 |
| f(x) |
-2 |
-5 |
-9 |
-12 |
-16 |
|
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