Consider the func y=3x^2-x^3
a) What is the equation of the tangent line to this function at the point (1,2) ?

Question

Consider the func y=3x^2-x^3
a) What is the equation of the tangent line to this function at the point (1,2) ?

accessdenied · Answer

Do you remember how to find the equation of a line using point-slope in Algebra?  It's very much like that, only we find the slope in a different way.

Point-slope: $y - y_1 = m(x - x_1)$
$m$ is the slope of the tangent line at $(1,2)$, or the derivative at x=3

accessdenied · Answer

x=1, not x=3 *

anonymous · Answer

To determine the equation of a line, you need SLOPE and a POINT on that line... In the question, you are given the point... How do you find the slope?  (Well, in calculus, the derivative determines the rate of change, slope, of a function at a given point)

anonymous · Answer

So, take the derivative of the equation..   6x - 3x^2... 
Then, plug in the x value of the point to find the slope at that point

anonymous · Answer

Taking (1, 2), plug in the x-value 1 ----  6(1) - 3(1)^2 = 3
So, the slope is 3 and a point on the line is (1, 2)...
Now, find the equation of the line!

anonymous · Answer

Thanks guys....!

accessdenied · Answer

You're welcome!  :)

anonymous · Answer

good luck!