Point of inflection question

  • Thread starter haris123
  • Start date
  • #1
9
0
If g(x) = xe^kx where k < 0 is a constant, then we may conclude that g has

(a) a relative maximum at x = -1/k (b) a relative minimum at x = -1/k
(c) a relative maximum at x = 1/k (d) a relative minimum at x = 1/k
(e) none of (a) - (d)
 

Answers and Replies

  • #2
9
0
i think the answer should be A
 
  • #3
Dick
Science Advisor
Homework Helper
26,263
619
i think the answer should be A

That would be right. But why do you think so?
 
  • #4
9
0
That would be right. But why do you think so?

the reason is because the graph is decreasing from - infinity to -1/k and increasing from -1/k to infinity. it changes from negative to positive. hence its a maximum. am i right?
 
  • #5
Dick
Science Advisor
Homework Helper
26,263
619
the reason is because the graph is decreasing from - infinity to -1/k and increasing from -1/k to infinity. it changes from negative to positive. hence its a maximum. am i right?

If that's what you think it does, you are wrong. Changing from decreasing to increasing sounds more like a minimum. Can't you give a reason in terms of derivatives?
 
  • #6
9
0
i am the one who needs help. so you tell me what do you think in terms of derivatives? btw from negative to positive is maximum
 
Last edited:
  • #7
1,384
0
You can find out if a point is max. or min. by two methods -

1) Check the sign of f'(x) to the left and right of the point. If it's sign is negative to the left and positive to the right, then the point is a local minima.

2) Find out the value of the second derivative at the given point and check its sign. If it is negative then the point is a local maxima. If it is positive then the point is a local minima.
 
  • #8
1,384
0
btw from negative to positive is maximum

If f'(x) changes sign from negative to positive as we go through a point from left to right, then that point is a minimum not maximum! Review your calculus notes
 

Related Threads on Point of inflection question

  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
3
Views
17K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
9
Views
1K
  • Last Post
Replies
2
Views
5K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
5
Views
2K
Top