# Finding the graph of a function with only derivative and domain.

#### mettler "The graph below is the graph of f', the derivative of f; The domain of the derivative -5≤x≤6"

1) The critical points for f are x=
2) The critical points for f' are x= -3, -2/3, 2, 4, 5.
3) F has a local maximum when x=
4) F has its maximum value on [-5,6] when x=
...
Is this information obtainable without knowing the original function or graphing the original function?
I would assume it is, but I'm not sure how to go about it?

#### MarkFL

1.) The critical points for f are where f' has its roots.

3.) f will have a local maximum where f' goes from positive to negative.

4.) Think about the integral of f', which is f. Is the area above the x-axis greater than the area below it to the left?

#### mettler

Thanks MarkFL2

4 as listed before.
10) Does f' have a minimum value on [-5,6]? Explain. (it doesnt look like it does?)
11) Does f'' have a miniumum value on [-5,6]? Explain. (it would have a maximum if anything)

The graph shows at -5,6 that it would go infinity to the left, wouldn't that stop any chance of a minimum being at that point?

#### MarkFL

4.) Which looks greater, the amount of decrease of f from x = -5 to 1 or the amount of increase from x = 1 to 3? This indicates that f must have an absolute maximum where?

10.) It appears the absolute minimum for f' on the given interval is at x = -2/3.

11.) Is there a place where the slope of f' is a minimum?

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#### mettler

Oh. I was thinking [-5,6] was an x and y coord.

4) x = 2
10) Yes, at x=-2/3 the graph of f' goes from decreasing to increasing showing there is a minimum.
11) Yes, at x= -2 the slope of f' changes from decreasing to increasing showing there is a minimum.

Does this look correct?

#### mettler

Also to just check.

Question 8) f' has its maximum value when x= ( I put -3, and 2). Where the slopes reach 0 while being concave down. Would this be correct? It threw me off because the question asks for 1 x value.

#### MarkFL

Just look at the graph, and find where the absolute maximum of f' occurs, since the graph is of f'.