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For the graph of f ( x ) shown above, sketch two functions F with F ?( x )= f (

ID: 2828934 • Letter: F

Question

For the graph of f(x) shown above, sketch two functions F with F?(x)=f(x). In one let F(0)=0; in the other, let F(0)=1. Mark x1, x2 and x3 on the x-axis of your graph. Identify local maxima, minima and inflection points of F(x).

(a) At which point does F(x) achieve its largest value?
A. x1
B. x2
C. x3

(b) At which point does F(x) achieve its smallest value?
A. x1
B. x2
C. x3

For the following questions, consider only the interior points on the domain on which f(x) is shown.
(c) How many critical points does F(x) have?
A. 0
B. 1
C. 2
D. 3
E. more than 3

(d) How many local maxima does F(x) have?
A. 0
B. 1
C. 2
D. 3
E. more than 3

(e) How many local minima does F(x) have?
A. 0
B. 1
C. 2
D. 3
E. more than 3

(f) How many inflection points does F(x) have?
A. 0
B. 1
C. 2
D. 3
E. 4

Explanation / Answer

1.a) x1

2. b)x2

3. c) 2

4.b) 1

5. b) 1

6. a)0