SOLUTION: Determine the equation of the tangent line to the curve 𝑦 = −𝑥 2 − 3𝑥 + 4 at 𝑥 = 2.

Algebra ->  Linear-equations -> SOLUTION: Determine the equation of the tangent line to the curve 𝑦 = −𝑥 2 − 3𝑥 + 4 at 𝑥 = 2.      Log On


   

Question 1205498: Determine the equation of the tangent line to the curve 𝑦 = −𝑥
2 − 3𝑥 + 4 at 𝑥 = 2.
Found 2 solutions by greenestamps, MathLover1:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


y=-x%5E2-3x%2B4
dy%2Fdx=-2x-3

At x=2...
y=-4-6%2B4=-6
dy%2Fdx=-4-3=-7

The equation of the tangent line to the curve at (2,-6) is

y=mx%2Bb
y=-7x%2Bb
-6=-7%282%29%2Bb
-6=-14%2Bb
b=8

y=-7x%2B8

ANSWER: y=-7x+8

A graph, showing a tangent at (2,-6)

graph%28400%2C400%2C-1%2C3%2C-15%2C1%2C-x%5E2-3x%2B4%2C-7x%2B8%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the equation of the tangent line to the curve
y+=+-x%5E2-+3x+%2B+4 at x=+2
The gradient of the tangent is equal to the derivative of the curve evaluated at the point where the curve and tangent line meet.
at x=+2 , y+=+-2%5E2-+3%2A2+%2B+4=-4-6%2B4=-6
point of tangency is at (2,-6)
y’ =+-2x-+3
compute the value of the derivative function at x=2
y'%282%29=-2%2A2-3=-7
so, slope is m=-7
use the point-slope formula of a line, substitute the values above
y-y1=m%28x-x1%29
y-%28-6%29=-7%28x-2%29
y%2B6=-7x%2B14
y=-7x%2B14-6
y=-7x%2B8=> tangent line