anonymous
  • anonymous
Below is the graph of f ′(x), the derivative of f(x), and has x-intercepts at x = –3, x = 1 and x = 2. There are horizontal tangents at x = –1.5 and x = 1.5. Which of the following statements is true?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
https://i.gyazo.com/f475d14cb58c410d88e94c4bef8cdb8d.png @jim_thompson5910 can you check for me?
jim_thompson5910
  • jim_thompson5910
go back to the previous problem. You did the first derivative test when you checked to see the sign changes in f ' (x) as it passed through x = 5
jim_thompson5910
  • jim_thompson5910
for this graph f ' (x) is positive when we're to the left of x = 1 f ' (x) is negative when we're to the right of x = 1

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More answers

jim_thompson5910
  • jim_thompson5910
|dw:1446680338553:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1446680379156:dw|
anonymous
  • anonymous
I get it but wouldn't the top of the curve represent a horizontal line?
anonymous
  • anonymous
|dw:1446680418898:dw| Slope at that point is 0
jim_thompson5910
  • jim_thompson5910
yeah but keep in mind that the graph they give you is of f ' (x) and not f(x)
jim_thompson5910
  • jim_thompson5910
the idea is to use f ' (x) to determine properties about f(x)
anonymous
  • anonymous
If that's the case, then I'd choose B due to the negative slope between -1.5 and 1.5
jim_thompson5910
  • jim_thompson5910
again, this graph is NOT f(x)
jim_thompson5910
  • jim_thompson5910
to figure out where f is decreasing, look where f ' (x) is negative ie where it is below the x axis
jim_thompson5910
  • jim_thompson5910
btw it is very common for students to mix up f and f ' so be sure to be careful about these types of problems when it comes to the exam
anonymous
  • anonymous
Ok, so looking at your graph and the info given, it has to be A.
anonymous
  • anonymous
@jim_thompson5910
jim_thompson5910
  • jim_thompson5910
the graph of f ' (x) is decreasing from x = -1.5 to x = 1.5 which means f '' (x) is negative from x = -1.5 to x = 1.5 so the graph of f(x) is concave down from x = -1.5 to x = 1.5

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