Question

For f(x)=2x+cot x on 0 13 years ago

Answer 1

1. Find the 2nd derivative by finding the 1st one and re-iterating the process once more.

https://docs.google.com/file/d/0Byzx8Bx-UMzba3hLZFowa1JSUzg/edit?usp=sharing


2. Find the roots for f'' by setting f''(x)=0. The root found is where the inflection point is.

https://docs.google.com/file/d/0Byzx8Bx-UMzbMkhRMWVuNGxsWGc/edit?usp=sharing


3. Determine whether x's to the left of any inflection point is positive(+) or negative(-). Do the same for the right side. We know we have an inflection point at x_0 if: the function is differentiable at x_0, f(x_0)=0, and the sign changes from (+) to (-) or vice versa.

https://docs.google.com/file/d/0Byzx8Bx-UMzbWldiU1NEUlRhb28/edit?usp=sharing


4. You should be able to answer your question.

5. Be sure to check your answer: https://www.desmos.com/calculator/q72k1sxdkj

Answer 2

Refer to the attachment.