Using the graph $g(x)$ to find intervals.

Question

I am having a bit of a struggle with my one math question.

https://i.stack.imgur.com/DE6OG.jpg

I was able to find a) b) c) but now that it asks for g'(x) I am running into a wall.

Could somebody help please.

Thanks!

score 1 · Answer 1 · answered Oct 10 '16 at 17:13

1

g'(x)>0 happens when the slope of g(x) is positive (increasing).

Therefore find the intervals where g(x) is increasing.

For example at (-6,-4), g'(x) is > 0.

answered Oct 10 '16 at 17:13

YangCPG

71

Ok that makes sense, but when I type in:
(-6,-4)U(2,4)

It tells me its not correct.
– Franky Oct 10 '16 at 17:30
Check the graph again, you're correct that the slope is positive in that interval but if you look again, the slope is actually positive starting at 0. – YangCPG Oct 10 '16 at 17:56
Of course, omg. Thanks so much! – Franky Oct 10 '16 at 17:59
Glad I could help :) – YangCPG Oct 10 '16 at 18:26

score 1 · Answer 2 · answered Oct 13 '16 at 13:22

1

g'(x) depicts the monotonicity of a function. If g'(x) is positive, it means that the curvature of the graph is strictly increasing between particular interval say;(x,y). If g'(x) is negative it indicates that the function g(x) is strictly decreasing between two points of inflection. And g'(x)=0 is the critical point. I.e. The points on the curve for which the slope at that very point is undefined or parallel to x-axis.

answered Oct 13 '16 at 13:22

Mihir

39

This is a little bit confused. $g'(x)$ being positive is not about the curvature of the graph of $g(x)$. Perhaps a bit of editing can salvage your effort, including some use of $\LaTeX$ to format the math expressions. See How to post mathematical expressions. – hardmath Oct 13 '16 at 15:08

Using the graph $g(x)$ to find intervals.

2 Answers2