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questions about graph-derivitive

Im working on my study guide..and I have no idea how to do these types of problems.Can anyone please just give me a hint on how I can approach these?

I attached the graph.

a few of the questions im having trouble with are:

At which point is f'(x)> 0?

a) A b) B c) C d) D e) None of these

At which point is f'(x) =0 ?

a) A b) B c) C d) D e) None of these

At point F, is:

a) concave up b) concave down c) neither, F is an inflection point d) None of these

Im not sure how to even begin on these. Derivatives confuse me.Any feedback would be appreciated!

Re: questions about graph-derivitive

Quote:

Originally Posted by

**salma** At which point is f'(x)> 0?

a) A b) B c) C d) D e) None of these

At which point is f'(x) =0 ?

a) A b) B c) C d) D e) None of these

At point F, is:

a) concave up b) concave down c) neither, F is an inflection point d) None of these

The derivative is all about slope of the tangent at a point.

Draw a tangent at each of those points.

If the slope is negative the derivative is negative.

If the slope is positive the derivative is positive.

If the slope is zero the derivative is zero.

If the graph is above the tangent means concave down and visa verse.

Re: questions about graph-derivitive

Ok I drew tangents on each of the points and got positive for point C,D,E, and H. Is this right or am i doing it wrong?

Re: questions about graph-derivitive

Quote:

Originally Posted by

**salma** Ok I drew tangents on each of the points and got positive for point C,D,E, and H. Is this right or am i doing it wrong?

No, not at all correct.

Slopes positive at $\displaystyle D,~G,~\&~H$

Slopes zero at $\displaystyle C,~E,~\&~F$

Re: questions about graph-derivitive

How does knowing the positive/negative slopes help with finiding where f '(x)>0? Does that mean where its postive, so the answer should be choice E right?

Re: questions about graph-derivitive

No, "f'(x)< 0" does NOT mean "it's positive"!