In Exercises 91–96 , the graph of a derivative f ′ is shown. Use the information in each graph to determine where f is increasing or decreasing and the x -values of any extrema. Then sketch a possible graph of f . Increasing on ( − 1 , ∞ ) , decreasing on ( − ∞ , − 1 ) , relative minimum at x = − 1 .
In Exercises 91–96 , the graph of a derivative f ′ is shown. Use the information in each graph to determine where f is increasing or decreasing and the x -values of any extrema. Then sketch a possible graph of f . Increasing on ( − 1 , ∞ ) , decreasing on ( − ∞ , − 1 ) , relative minimum at x = − 1 .
Solution Summary: The author analyzes the graph of the derivative function fprime and determines whether the function is decreasing or increasing.
In Exercises 91–96, the graph of a derivative
f
′
is shown. Use the information in each graph to determine where f is increasing or decreasing and the x-values of any extrema. Then sketch a possible graph of
f
.
Increasing on
(
−
1
,
∞
)
, decreasing on
(
−
∞
,
−
1
)
, relative minimum at
x
=
−
1
.
4
In the integral dxf1dy (7)², make the change of variables x = ½(r− s), y = ½(r + s), and
evaluate the integral. Hint: Find the limits on r and s by sketching the area of integration in the (x, y) plane along
with the r and s axes, and then show that the same area can be covered by s from 0 to r and r from 0 to 1.
7. What are all values of 0, for 0≤0<2л, where 2 sin² 0=-sin?
-
5π
6
π
(A) 0, л,
and
6
7π
(B) 0,л,
11π
, and
6
6
π 3π π
(C)
5π
2 2 3
, and
π 3π 2π
(D)
2' 2'3
, and
3
4元
3
1
די
}
I
-2m
3
1
-3
บ
1
#
1
I
3#
3m
8. The graph of g is shown above. Which of the following is an expression for g(x)?
(A) 1+ tan(x)
(B) 1-tan (x)
(C) 1-tan (2x)
(D) 1-tan
+
X
-
9. The function j is given by j(x)=2(sin x)(cos x)-cos x. Solve j(x) = 0 for values of x in the interval
Quiz A: Topic 3.10
Trigonometric Equations and Inequalities
Created by Bryan Passwater
can you solve this question using the right triangle method and explain the steps used along the way
Chapter 3 Solutions
Pearson eText Calculus and Its Applications, Brief Edition -- Instant Access (Pearson+)
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