Friday

July 25, 2014

July 25, 2014

Posted by **cel** on Monday, November 29, 2010 at 9:31pm.

All I know is that it has something to do with the Mean Value Theorem/Rolle's Theorem.

- AP Calculus -
**Reiny**, Monday, November 29, 2010 at 11:25pmYou must have a typo.

There are all kinds of values of c for which the above equation has 3 roots.

e.g. if c=0

x^3 - 15x = 0

x(x^2 - 15) = 0

x = 0 or x = ± √15

are you sure it wasn't x^3 + 15x + c = 0 ?

I will assume it was

It's been 50 years but if I recall, Rolle's theorem says that if there are two x-intercepts , then the derivative must be zero between those two points

so let f(x) = x^3 + 15x + c

f '(x) = 3x^2 +15 = 0

notice this is always positive, since x^2 = -5 has no real solution,

so there are no turning points, and the curve cuts only once.

You do know that every cubic must cut he x-axis at least once?

- AP Calculus -
**Alon**, Thursday, December 8, 2011 at 2:21amThe missing info it the interval [-2,2]. In this interval there could be just one root.

**Related Questions**

Calculus - Let f(x)=3x^5+5x^3+15x+15. Use Rolle's Theorem to show that f(x) has ...

Math - Calculus - Show that the equation x^3-15x+c=0 has at most one root in the...

math - 4.2 18. show that the equation 2x-1-sinx=0 has exactly one real root.

Algebra - For what value(s) of b will x^2 + bx + 3 have exactly one root? I'm ...

math - show that the equation x^3-15x+c=0 has at most one root on the interval...

Math - Show that the equation x^3-15x+c=0 has at most one root in the interval...

calc - Show that the equation x^3-15x+c=0 has at most one root in the interval...

Math - For what value of k does the equation x2 + k = kx – 8 have: Two distinct ...

math - show that the equation 2x-1-sinx=0 has exactly one real root. sin x = 2x-...

Math - Calculus - Show that the equation x^3-15x+c=0 has at most one root in the...