Expert: Ahmed Salami - 2/13/2011

Question
Hello Ahmed,

I was wondering if you could help answer this question:

If y = 3x^2 - 4 and a tangent line exists along this graph with a slope of -12, what would be the corresponding point on this tangent line?

I have not yet learned derivatives in class yet so if that is part of the solution, could you explain what that is to me? Your help is appreciated!

Answer
Hi Kim,
y = 3x² - 4 has a slope function
dy/dx = 6x
which means that at any point the slope of the tangent line is 6 times the value of x at that point.
So, if the slope is -12 at a point, then
6x = -12
x = -2
and
y = 3(-2)² - 4
= 3(4) - 4
= 12 - 4
= 8

Therefore, the point of the curve where the slope is -12 is (-2,8).

Regards