Derivative graphs

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How would the approximate graph of the derivative of the following function look?

First of all, I don't know where to start from. I am able to relate to the fact that the derivative's graph will have negative values wherever there is a ngegative slope and positive values wherever there is a positive slope. So I thought for the first curved part (starting from the left), the gradient goes less and less positive until the turning point, where it goes more and more negative until it becomes undefined. I'm stuck there.

Thanks in advance, Ramana

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1 Answer

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It should look like this

From left to right (x).

1. The slope is infinite as graph is almost vertical.
2. The slope decreases and becomes zero. - hence the derivative is zero.
3. Again slope decreases and function becomes vertical - derivative tends to - inf - and not defined.
4. Slope starts increasing and becomes less negative.
5. At x = 0 - slope is zero.
6. At +ve x - the curvature changes from concave up to concave down - hence maxima
7. Another place where gradient zero
8. Gradient again goes to -ve infinity

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