1225FormA

6. Suppose that

• f is a continuous, real-valued function on the closed interval [ a, b ] and • f has an absolute minimum at x = c , where a < c < b .

Consider the following statements about f :

Statement I: f ( c ) ≤ f ( x ) for all x in [ a, b ]. Statement II: f has an absolute maximum on [ a, b ].

Which of the above statements MUST be TRUE ?

(A) Statement I only (B) Statement II only

(C) both Statement I and Statement II (D) neither Statement I nor Statement II

7. Suppose f is continuous on ( −∞ , ∞ ) and the graph of its derivative, y = f ′ ( x ), is shown below.

y

3

y = f ′ ( x )

2

1

x

1

2

3

4

5

6

Which of the following MUST be FALSE about the function f ?

(A) f has a critical number at x = 3. (B) f has an inflection point at x = 3. (C) f has a critical number at x = 4 . 5. (D) f is concave up on (1 , 3).

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