The graph of the derivative f of a continuous function f is shown below. (Assume

Question

The graph of the derivative f of a continuous function f is shown below. (Assume p continues toinfinity.) On what interval is f increasing? (Enter your answer in interval notation.) On What interval is f decreasing? (Enter your answer in interval notation.) At what value(s) of x does f have a local maximum? (Enter your answers as a comma-separated list.) At what value(s) of x does f have a local minimum? (Enter your answers as a comma-separated list.) On what interval is f concave upward? (Enter your answer in interval notation.) On what interval is f concave downward? (Enter your answer in interval notation.) What are the x-coordinate(s) of the inflection point(s) off? (Enter your answers as a comma-separated list.) Assuming that f(0) = 0, sketch a graph off. (Do this on paper. Your teacher may ask you to turn in this work.)

Explanation / Answer

a) when f'(x) > 0 , then f is increasing => (0,2) U (4, 6) U (8 , infinity )
When f'(x) < 0 , then f is decreasing => (2,4) U (6,8)
b) Since derivative is changing sign from +ve to -ve at x=2 , hence local maxima.
   Since derivative is changing sign from -ve to +ve at x=4 and x=8 , so x=4,8              could be local minima.
c) slope of f'(x) is positive for ( 3 , 6 ) U (6, infinity ) , Hence concave up
   slope of f'(x) is negative for ( 0 , 3 ) , Hence concave down.
d) At x= 3 slope of f'(x) is 0, hence x=3 is point of inflection.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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