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I have the graph below:

Graph of fx

The question is asking to estimate values of $x$ between $0$ and $6$ where derivative of $f$ is $2$. I also got the answer as well which says $x$ is $4.2$ and $5.6$:

enter image description here

My question is, what is the point of this question? What should I look for? How the answer is $4.2$ and $5.6$?

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The point of the question is to drive home the interpretation of derivative as slope, and to see if you understand what the slope of a graph is.

You should look for points on the curve where the slope (of the tangent line) seems to be about 2. Look at the higher red line on your diagram - it goes over 1 and up 2, which is slope 2, which is what you are looking for.

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    If all you are given is a graph, then, yes, the natural assumption is that it is a visual problem and there are no equations available for you to use.2012-04-12