Complete the following table For parts A thru D: When the derivative function, f

Question

Complete the following table

For parts A thru D:

When the derivative function, f' is...

Then the values of

the second derivative

function f'', are

(i) positive, or

(ii) negative

And the original function, f, is:

(i) Decreasing and concave up,

(ii) Decreasing and concave up,

(iii) Increasing and concave up, or

(iv) Increasing and concave down

For parts E thru H:

When the derivative function, f' is...

Then the values of

the second derivative

function f'', are

(i) From positive to negative, or

(ii) From negative to positive

And the original function, f, is:

(i) Decreasing changing from concave up to concave down,

(ii) Decreasing changing from concave down to concave up,

(iii) Increasing changing from concave up to concave down, or

(iv) Increasing changing from concave down to concave up

For parts A thru D:

When the derivative function, f' is...

Then the values of

the second derivative

function f'', are

(i) positive, or

(ii) negative

And the original function, f, is:

(i) Decreasing and concave up,

(ii) Decreasing and concave up,

(iii) Increasing and concave up, or

(iv) Increasing and concave down

A. Negative and Increasing B. Positive and Increasing C. Positive and Decreasing D. Negative and Decreasing

For parts E thru H:

When the derivative function, f' is...

Then the values of

the second derivative

function f'', are

(i) From positive to negative, or

(ii) From negative to positive

And the original function, f, is:

(i) Decreasing changing from concave up to concave down,

(ii) Decreasing changing from concave down to concave up,

(iii) Increasing changing from concave up to concave down, or

(iv) Increasing changing from concave down to concave up

E. Positive & Decreasing, then Positive & Increasing. F. Positive & Increasing, then Positive & Decreasing G. Negative & Decreasing, then Negative & Increasing H. Negative & Increasing, then Negative & Decreasing

Explanation / Answer

A. positive decreasing and concave up
B. positive       increasing and concave up
c. negative       increasing and concave down
d. negative       decreasing and concave down

E. negative to positive   increasing changing from concave down to concave up
F. positive to negative   increasing changing from concave up to concave down
G. negative to positive   decreasing changing from concave down to concave up
H. positive to negative   decreasing changing from concave up to concave down

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