SOLUTION: The equation of a curve is given by y = 6x^5+12 Obtain the tangent line to the curve at the point where x = 3. Please enter your answer as an equation in the form: y = m x +

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The equation of a curve is given by y = 6x^5+12 Obtain the tangent line to the curve at the point where x = 3. Please enter your answer as an equation in the form: y = m x +       Log On


   

Question 869493:
The equation of a curve is given by
y = 6x^5+12
Obtain the tangent line to the curve at the point where x = 3. Please enter your answer as an equation in the form: y = m x + c
for some constants m, c.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Find derivative and then compute this a the slope using x=3.
dy%2F%28dx%29=30x%5E4
dy%2F%28dx%29%283%29=30%2A3%5E4
value of derivative there, is 2430.

Find the y value at x=3 so you know what point this tangent line intersects.
y=6%2A3%5E5%2B12
y=1470

Find the y-intercept for the tangent line at point (3, 1470).
highlight_green%28y=2430x%2Bb%29
solve for b using the point.


I used "b" instead of "c".