Prove that has exactly two solutions.

Proof so far.

Now , set it equals to zero, we have , so this equation have 3 solutions, meaning we have 3 extremas, meaning the equation can cross the x-axis twice.

Would that be enough to prove it?

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- Nov 13th 2008, 06:43 AMtttcomraderNumber of solutions
Prove that has exactly two solutions.

Proof so far.

Now , set it equals to zero, we have , so this equation have 3 solutions, meaning we have 3 extremas, meaning the equation can cross the x-axis twice.

Would that be enough to prove it? - Nov 13th 2008, 07:21 AMArch_Stanton

The derivative is always positive, so value of this finction constantly rises and there's just one root (solution).

Is that what you meant? - Nov 13th 2008, 07:34 AMHallsofIvy
No, that is NOT f', it is just f itelf!

Quote:

, set it equals to zero, we have , so this equation have 3 solutions, meaning we have 3 extremas, meaning the equation can cross the x-axis twice.

Would that be enough to prove it?

- Nov 13th 2008, 07:36 AMtttcomrader
Oh, it should have been , I accidentally put in the derivative instead of the original function.