Sketch the graph of a function f that satisfies the following conditions: • The function is continuous everywhere • The function is not differentiable at x = 0 • x-intercepts are x= 0 and x=8 • y-intercept (0, 0) •f ' 0 on (0,[16/5]); f ' 0 on (−∞, -[8/5]) f"

Question

Sketch the graph of a function f that satisfies the following conditions: • The function is continuous everywhere • The function is not differentiable at x = 0 • x-intercepts are x= 0 and x=8 • y-intercept (0, 0) •f ' 0 > on (0,[16/5]); f ' 0 < on (−∞ ,0), ([16/5] ,∞) •f '' 0 > on (−∞, -[8/5]) f"<0 on (-[8/5],0) , (0,∞) Be sure to label any relative maxima/minima and any points of inflection. My teacher has not showed us how to make these kind of graphs! I don't know how to make it with the info given! PLEASE HELP!! Can anyone explain to me and show me a graph for this?

wolf1728 · Answer

I think the function would be differentiable at x=0.  Perhaps it wouldn't be differentiable at a point at a point where the slope is perfectly vertical or infinite?

anonymous · Answer

Have a look at this video explanation http://www.khanacademy.org/math/calculus/differential-calculus/visualizing-derivatives-tutorial/v/where-a-function-is-not-differentiable