SOLUTION: The equation of a curve is given by y = 4x^4+10 Obtain the tangent line to the curve at the point where x = 2. Please enter your answer as an equation in the form: y = m x + c

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The equation of a curve is given by y = 4x^4+10 Obtain the tangent line to the curve at the point where x = 2. Please enter your answer as an equation in the form: y = m x + c       Log On


   

Question 967188: The equation of a curve is given by
y = 4x^4+10
Obtain the tangent line to the curve at the point where x = 2. Please enter your answer as an equation in the form: y = m x + c
for some constants m, c.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
dy%2Fdx=%28d%2Fdx%29%284x%5E4%2B10%29

dy%2Fdx=16x%5E3%2B0

At x=2,
dy%2Fdx=16%2A%282%29%5E3=16%2A8=highlight_green%28128%29, the slope of the tangent line at x=2.

The y coordinate for x=2, according to the given degree-four equation is 4%2A%282%29%5E4%2B10=highlight_green%2874%29.

You want the equation of the tangent line at point (2,74) and slope 128. You can use point-slope form to continue...
highlight_green%28y-74=128%28x-2%29%29.....