f(t) dt, where f is the function whose graph is shown below. You can assume the graph off is symmetric across the y-axis.Let g(x)(a) Evaluate g(-3) and g(3)g(-3)g(3)(b) Estimate g(-2), g(-1), and g(0) to the nearest half-unit.g(-2)g(-1)g(0)(c) Determine the x-interval on which g is increasing. Ifg is never increasing, type "N" in each blankx-interval< x<(d) Where does g have its maximum value?х%3Graph of f:110

Question
Asked Nov 22, 2019
7 views
f(t) dt, where f is the function whose graph is shown below. You can assume the graph off is symmetric across the y-axis.
Let g(x)
(a) Evaluate g(-3) and g(3)
g(-3)
g(3)
(b) Estimate g(-2), g(-1), and g(0) to the nearest half-unit.
g(-2)
g(-1)
g(0)
(c) Determine the x-interval on which g is increasing. Ifg is never increasing, type "N" in each blank
x-interval
< x<
(d) Where does g have its maximum value?
х%3
Graph of f:
1
1
0
help_outline

Image Transcriptionclose

f(t) dt, where f is the function whose graph is shown below. You can assume the graph off is symmetric across the y-axis. Let g(x) (a) Evaluate g(-3) and g(3) g(-3) g(3) (b) Estimate g(-2), g(-1), and g(0) to the nearest half-unit. g(-2) g(-1) g(0) (c) Determine the x-interval on which g is increasing. Ifg is never increasing, type "N" in each blank x-interval < x< (d) Where does g have its maximum value? х%3 Graph of f: 1 1 0

fullscreen
check_circle

Expert Answer

Step 1

(a) The figure is shown below:

g(-3) 0
3
3
2
1
-3 -2-10 12 3 t
-2
-3
help_outline

Image Transcriptionclose

g(-3) 0 3 3 2 1 -3 -2-10 12 3 t -2 -3

fullscreen
Step 2

(b)

(b) We need to evaluate the area under the curve according to the following graph
sdt=2.5
fdt 1.5
Thus
g(-2) f
or,g(-2)
1
g(-1) f)dt 1+2.5
or,g(-1) 3.5
0
g(0) = f()dt 3.5+1.5= 5
or, g(0) 5
help_outline

Image Transcriptionclose

(b) We need to evaluate the area under the curve according to the following graph sdt=2.5 fdt 1.5 Thus g(-2) f or,g(-2) 1 g(-1) f)dt 1+2.5 or,g(-1) 3.5 0 g(0) = f()dt 3.5+1.5= 5 or, g(0) 5

fullscreen
Step 3

(c)

...
(c) If we differentiate g(x) we will get f(x)
Thus, according to the fundamental theorem of calculus, if g'(x) = f(x)
then, g(x) will be increasing if and only if f (x) is positive and
We can see that f(x) is positive from (-3,0)
Thus, g(x) is increasing on the interval (-3,0)
x -interval -3<x<0
help_outline

Image Transcriptionclose

(c) If we differentiate g(x) we will get f(x) Thus, according to the fundamental theorem of calculus, if g'(x) = f(x) then, g(x) will be increasing if and only if f (x) is positive and We can see that f(x) is positive from (-3,0) Thus, g(x) is increasing on the interval (-3,0) x -interval -3<x<0

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Derivative