Josephood7

Below is the graph of the derivative f′(x)f′(x) of a function defined on the interval (0,8). You can click on the graph to see a larger version in a separate window.

Refer to the graph to answer each of the following questions. For parts (A) and (B), use interval notation to report your answer. (If needed, you use U for the union symbol.)

(A) For what values of xx in (0,8) is f(x)f(x) increasing? (If the function is not increasing anywhere, enter None .)

Answer: 
(B) For what values of xx in (0,8) is f(x)f(x) concave down? (If the function is not concave down anywhere, enter None .)

Answer: 
(C) Find all values of xx in (0,8) is where f(x)f(x) has a local minimum, and list them (separated by commas) in the box below. (If there are no local minima, enter None .)

Local Minima: 
(D) Find all values of xx in (0,8) is where f(x)f(x) has an inflection point, and list them (separated by commas) in the box below. (If there are no inflection points, enter None .)

Inflection Points: 

Let f(x)=5x2x2+3f(x)=5x2x2+3

Below, type none if there are none.

Input the interval(s) on which ff is increasing.

Input the interval(s) on which ff is decreasing.

Find the point(s) at which ff achieves a local maximum.

Find the point(s) at which ff achieves a local minimum.

Find the interval(s) on which ff is concave up.

Find the interval(s) on which ff is concave down.

Find all inflection points.

For the function ff given above, determine whether the following conditions are true. Input T if the condition is ture, otherwise input F .

(a) f′(x)<0f′(x)<0 if 0<x<20<x<2; 
(b) f′(x)>0f′(x)>0 if x>2x>2; 
(c) f′′(x)<0f″(x)<0 if 0≤x<10≤x<1; 
(d) f′′(x)>0f″(x)>0 if 1<x<41<x<4. 
(e) f′′(x)<0f″(x)<0 if x>4x>4; 
(f) Two inflection points of f(x)f(x) are, the smaller one is x=x=  and the other is x=

For x∈[−15,14]x∈[−15,14] the function ff is defined by

On which two intervals is the function increasing?
 to 
and
 to 
Find the region in which the function is positive:  to 
Where does the function achieve its minimum?