SOLUTION: Please help me If f(x) = 6x2 − x3, find f '(1) and use it to find an equation of the tangent line to the curve y = 6x2 − x3 at the point (1, 5).

Algebra ->  Functions -> SOLUTION: Please help me If f(x) = 6x2 − x3, find f '(1) and use it to find an equation of the tangent line to the curve y = 6x2 − x3 at the point (1, 5).      Log On


   

Question 1153277: Please help me
If
f(x) = 6x2 − x3,
find f '(1) and use it to find an equation of the tangent line to the curve
y = 6x2 − x3
at the point (1, 5).
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Use "^" (shift-6) to denote exponents.

Your function is y = 6x^2-x^3.

y+=+6x%5E2-x%5E3
dy%2Fdx+=+12x-3x%5E2

At x=1, the derivative (slope) is 12(1)-3(1^2) = 12-3 = 9.

The equation of the tangent line at (1,5) is y = 9x-4.

A graph, showing the function and the tangent line at (1,5):

graph%28400%2C400%2C-5%2C5%2C-15%2C35%2C6x%5E2-x%5E3%2C9x-4%29