Question

In: Math

1. True or False: If we know that f(x) is increasing on an interval, then f...

1. True or False:

If we know that f(x) is increasing on an interval, then f ''(x) should be positive on that interval.

2. True or False:

If f '(x) is increasing on a certain interval, then f ''(x) is positive on that interval.

3. If f ''(x)<0 on a certain interval, which of the following must be true on that interval? (2 answers)

A. f '(x) is decreasing

B. f(x) is increasing

C. f(x) is concave down

D. f(x) is concave up

E. f(x) is decreasing

F. f '(x) is concave down

G. f(x) is negative

H. f '(x)<0

4. At an inflection point...

A. f(x) has a horizontal tangent line

B. f '(x) = 0

C. f ''(x) = 0

D. f(x) = 0

E. f(x) has a vertical slope

5. If f '(a) = 0 and f ''(a) > 0, then...

A. f(a) is a local minimum

B. f(a) is an inflection point

C. f(a) is a critical point, but we can't determine if it is a max or min

D. f(a) is a local maximum

6. Either the First Derivative or the Second Derivative Test may be used to find local extrema.

True or False

7. Every critical point is a local extrema.

True or False

8. For the function f(x)=x^5-3x^2, x=1 is a local min.

True or False

9. For the function f(x)=x^5-3x^2, x=1 is a global min.

True or False

Solutions

Expert Solution

milcah answered 1 year ago

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