Question

Find the points on the graph of f(x)=2x^3+12x^2-126x+12 where the tangent is horizontal. List the x-values of these points.

Answer 1

The derivative of f gives you the slope of any tangent line along it.

A line with slope zero is a horizontal line.
So you want to find where f'(x)=0 (where the slope of the tangent line is horizontal).

Answer 2

So find f'(x) first, are you comfortable with the power rule? :)

Answer 3

6(x^2+4x-21)?

Answer 4

yah looks good! c:

Answer 5

now what

Answer 6

So you found an equation for the slope of a tangent line. Now we need to know where the graph has a slope of 0.
Let f'(x)=0 ---> 0=6(x^2+4x-21) andddd solve for x

Answer 7

-7 and 3... thanks! :)