Show work please.
2006-09-20 13:59:42 · 6 answers · asked by southsnow88 1 in Education & Reference ➔ Higher Education (University +)
its not written wrong... and im not cheating on homework... im studying for a test and dont get this problem
2006-09-20 14:18:44 · update #1
You need to find out where the derivative of f equals zero. The derivative means the rate of change, but it also means the slope of the tangent line. A horizontal line has a slope of zero.
f'(x)=3x^2+6x+1
Solve
3x^2+6x+1=0
Use the quadratic formula:
x = (-6+/-sqrt(36-12))/6
I'll let you finish figuring out that one yourself. You should be able to confirm these results on a graphing calculator.
2006-09-20 14:19:49 · answer #1 · answered by just♪wondering 7 · 0⤊ 0⤋
A horizontal tangent means zero slope. So, lets find the derivative of f(x)
f'(x) = 3x^2 + 6x + 1
solve for the roots
3x^2 + 6x + 1 = 0
x^2 + 2x + 1/3 = 0
completing the square,
(x+1)^2 + 1/3 - 1 = 0
(x+1)^2 = 2/3
x+1 = +/- sqrt(2/3)
x= -1 +/- sqrt(2/3)
Good luck!
2006-09-20 21:18:13 · answer #2 · answered by alrivera_1 4 · 0⤊ 0⤋
I just want to add one thing. If the tangent is horizontal, it does mean that the derivative is equal to zero. However, a derivative of zero doesn't mean that the tangent is zero. It could be a ponit of inflectin, which -- technically -- isn't a tangent. I don't think it is an issue for this problem.
2006-09-20 21:29:00 · answer #3 · answered by Ranto 7 · 0⤊ 0⤋
Differentiate f(x) once and set it to 0, then solve for x.
2006-09-20 21:18:56 · answer #4 · answered by Jacob Gan 2 · 0⤊ 0⤋
i think u wrote the question wrong, its not tangent...
2006-09-20 21:06:58 · answer #5 · answered by .: ZEIDO :. 3 · 0⤊ 0⤋
you shouldnt be cheatin on your maths homework.. lol
2006-09-20 21:07:49 · answer #6 · answered by xprincessxkellyx 1 · 0⤊ 0⤋