Find all relative minimum or maximum values as well as the x-values at which they occur. State each function is increasing or decreasing. Then sketch a graph of the function f ( x ) = 16 x 2 + 4
Find all relative minimum or maximum values as well as the x-values at which they occur. State each function is increasing or decreasing. Then sketch a graph of the function f ( x ) = 16 x 2 + 4
Solution Summary: The author calculates the relative minimum or maximum values of the function f(x)=16x 2+4 as well as the x- values at which
Find all relative minimum or maximum values as well as the x-values at which they occur. State each function is increasing or decreasing. Then sketch a graph of the function
Find the area of the shaded region.
(a)
5-
y
3
2-
(1,4)
(5,0)
1
3
4
5
6
(b)
3 y
2
Decide whether the problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to
estimate the solution.
STEP 1: Consider the figure in part (a). Since this region is simply a triangle, you may use precalculus methods to solve this part of the problem. First determine the height of the triangle and the length of the triangle's base.
height 4
units
units
base
5
STEP 2: Compute the area of the triangle by employing a formula from precalculus, thus finding the area of the shaded region in part (a).
10
square units
STEP 3: Consider the figure in part (b). Since this region is defined by a complicated curve, the problem seems to require calculus. Find an approximation of the shaded region by using a graphical approach. (Hint: Treat the shaded regi
as…
Solve this differential equation:
dy
0.05y(900 - y)
dt
y(0) = 2
y(t) =
Suppose that you are holding your toy submarine under the water. You release it and it begins to ascend. The
graph models the depth of the submarine as a function of time.
What is the domain and range of the function in the graph?
1-
t (time)
1 2
4/5 6 7
8
-2
-3
456700
-4
-5
-6
-7
d (depth)
-8
D: 00 t≤
R:
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
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