Saturday

July 26, 2014

July 26, 2014

Posted by **Joe** on Sunday, November 13, 2011 at 5:49pm.

Use Rolle's Theorem to show that f(x) has exactly one root.

- Calculus -
**Damon**, Sunday, November 13, 2011 at 5:58pmf' = 15 x^4 + 15 x^2 + 15

= 15 (x^4+x^2+1)

where is that slope = 0?

x^2 = [ -1 +/- sqrt(1-4)]/ 2

x^2 = -1/2 +/- (1/2) sqrt (-3)

complex roots only, it never has zero slope so it can only cross the axis once by Rolle's theorem. Once it crosses the axis, it can never reverse and come back.

**Related Questions**

AP Calculus - Show that the equation x^3 - 15x + c = o has exactly one real root...

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

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

calculus - Show that the function f(x)=4x^3−15x^2+9x+8 satisfies the ...

calc - Verify that the function satisfies the three hypotheses of Rolle's ...

calc - Verify that the function satisfies the three hypotheses of Rolle's ...

Calculus - Determine whether Rolle's Theorem can be applied to f on the closed ...

URGENT!! PLEASE Calc - Verify that the function satisfies the three hypotheses ...

Calculus (Please Check) - Show that the equation x^5+x+1 = 0 has exactly one ...

Calculus - Show that the function f(x)= x^(3) +3/(x^2) +2 has exactly one zero ...