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I know that when the function is increasing, the derivative is positive. What I am confused about for the first one is that when I am sketching the derivative, I don't know what direction it goes (even though i know it is positive). What I am thinking is that where the graph has a min or max, then the derivative must have an x-intercept there. That is how I came up with my graph for the first two questions.

For the third question, I tried doing the opposite. So the derivative is positive thus the function is increasing and vice versa. Where the derivative has an x-intercept, the function has a min or max but the question is still a little confusing to me.

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I think it would be helpful for you to discretize your graph along X axis and calculate the derivative using some finite differences formula.

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  • $\begingroup$ it has to be a sketch. i do not have time on a test to do finite differences formula $\endgroup$ – user8358234 Jan 24 at 13:32
  • $\begingroup$ So in this case, focus on the extreme values of the function f, the derivative there must be zero. Then consider the curvature as well, the more the function is convex, the more the derivative increases rapidly. $\endgroup$ – yas are Jan 24 at 13:37
  • $\begingroup$ i mentioned in my question that i did that. i want to know if my answers are correct and if not then how can i fix it $\endgroup$ – user8358234 Jan 24 at 13:43
  • $\begingroup$ Could you please post your answer using a paper with markers so as we can see the correspondences? $\endgroup$ – yas are Jan 24 at 14:10
  • $\begingroup$ okay i will do that $\endgroup$ – user8358234 Jan 24 at 14:13

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