Question

Find all the values of x where the graph of f(x) = 2 x^3 - 39 x^2 + 180 x - 4 has a horizontal tangent line.

Answer 1

find the 1st derivative...

let it equal zero and then solve for x

Answer 2

f'(x)=6x^2+78x+180=0

Answer 3

I am solving for x now =, thanks!

Answer 4

thats a start now solve for x

Answer 5

except I think its

\[f'(x) = 6x^2 - 78x + 180\]

Answer 6

oh yeah typo, thanks for catching that.

Answer 7

x=3 and x=10. Does that sound right?

Answer 8

yes thats fine... the curve has 2 stationary points (a max and a min) these points are where the tangent has a zero gradient

Answer 9

perfect thanks!

Answer 10

glad to help