Question

find the points on the graph at which the tangent is horizontal: (a) -x^3+x^2+5x-1

Answer 1

what class are you in?

Answer 2

Differentiate and equate to 0

Answer 3

http://www.wolframalpha.com/input/?i=derivative%28-x%5E3%2Bx%5E2%2B5x-1%29+%3D+0

Answer 4

(1, -4), (5/3, 148/27)

Answer 5

i am in college doing calculus now

Answer 6

\[\large f(x) = x^3+x^2+5x-1\]\[\large f'(x)= 3x^2 +2x +5\] equal derivative to 0. \[\large f'(x)=3x^2+2x+5=0\]\[\large 3x^2+2x+5 =0\]\[\large 3(x^2+\frac{2}{3}x)+5 = 0\]\[\large3(x^2+\frac23x +\frac19- \frac19)+5=0\]\[\large3(x+\frac13)^2+5 -\frac39=0\]\[\large 3(x+\frac13)^2+\frac{14}{3}=0\]Can you solve for x?