Below is the graph of the derivative f\'(x) of a function defined on the interva

Question

Below is the graph of the derivative 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.) For what values of x in (0, 8) is f(x) increasing? (If the function is not increasing anywhere, enter None) For what values of x in (0, 8) is f(x) concave down? (If the function is not concave down anywhere, enter None) Find all values of x in (0, 8) is where f(x) has a local minimum, and list them (separated by commas) in the box below. (If there are no local minima, enter None) Find all values of x in (0, 8) is where f(x) has an inflection point, and list them (separated by commas) in the box below. (If there are no inflection points, enter None)

Explanation / Answer

A)

if f'(x)>0 increasing else if f'(x)<0 decreasing..therefore at 0,1,2,3 function is increasing

B)

We will say that the graph of f(x) is concave up on interval iff f '(x) is increasing on interval

We will say that the graph of f(x) is concave down on interval iff f '(x) is decreasing on interval

therefore the points for concave down are 2,3,4

D) Usually graphs have regions which are concave up and others which are concave down. Thus there are often points at which the graph changes from being concave up to concave down, or vice versa. These points are called inflection points

therefore the values are 1,4,5,6

C)

local minimum where the graph changes from decreasing to increasing

that is at 4,6

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.