Question

Ap calc question about 1st derivative:

Answer 1

I understand part a but not part b

Answer 2

a relative minimum or max is when g'(x)=0 (if you dont know why ill explain it to you but you should) and as you see at -1 g'(-1)=0 so indeed there exists a min or max

Answer 3

@joyraheb we're looking at \(x=1\), not \(-1\), but the reasoning remains the same.

Also, we can precisely say whether we have a minimum or a maximum. To the left of \(x=1\), we have \(g'<0\) and to the right, we have \(g'>0\). So...

Answer 4

@SithsandGiggles oh my bad i saw it -1 but after all the explanation remains the same since at 1 also g'(1)=0 and concerning your explanation no need for all that its just g'(x)=0 because the slope of the tangent at a min or max of g(x) is 0 since its parallel to the x-axis. Thats it .

Answer 5

@SithsAndGiggles

Answer 6

Right, we're agreed on why there is an extremum, but for the rest I would disagree. The way the question is phrased (whether \(g\) has a relative maximum, minimum, or neither) suggests to me that they're looking for something more than a yes or no answer. After all, this is an AP test question. More detailed answers are more likely to get better scores.