Question

Determine the point(s) on the curve f(x) = 12x2 − 9x + 3 whose tangent is parallel to
y = 1 − 7x.

Answer 1

\(\large y=-7x+1\) is a line with slope \(\large -7\).

We want to know at what points along our curve f(x) will the line tangent to the curve have the same slope value.

Maybe that's a sloppy way of saying that.
The derivative of the function at a particular point represents the `slope` of the function at that point.

So we'll want to find the derivative of f(x) and then figure out where (at what x values) it is equal to -7.

Answer 2

Are you able to find the derivative of f(x) alright?

Answer 3

24x-9

Answer 4

thx :D

Answer 5

\(\large f'(x)=24x-9\)

Ok, good :)
So we're being asked, at what x values does this derivative (the slope of the tangent line), equal -7.

\[\large -7=24x-9\]

Answer 6

i racalled

Answer 7

Ok you got it now? :) cool

Answer 8

when it (tangent) is perpendicular m1x m2=-1 right?

Answer 9

m is a slope

Answer 10

Yah that sounds right :)
I usually see it written as \(\large m_2=-\dfrac{1}{m_1}\)

but ya you've got the right idea.

Answer 11

thank very much :)