I'm confused about this. How do you find the x values in this problem?

Sketch the graph of f(x) = x - 3x^2 and find the values of x for which the tangent line is horizontal

when the tangent line is horizontal, it means the slope of the tangent line is 0. so you can take the derivative of f(x) and set it equal to 0.

if you're referring to the graph, take a look at it:
https://www.google.com/search?q=graph%20of%20f(x)%20=%20x%20-%203x%5E2

if you draw tangent lines, you'll see the tangent line is horizontal at the peak.



This post was edited by carteblanche on Sep 5 2015 07:50pm

^ What he said about tangents

To sketch the function:

1. Decide what shape the function is by looking at the highest power of x and its sign
In this case, it's a parabola (highest power is 2) and it's upside down (sign is negative).

2. Find the x intercepts by factorizing the function and solving f(x)=0.
f(x)=x-3x^2=x(1-3x)
At f(x)=0, x=0 or 1/3