SOLUTION: Let f(x) = x^2 - 7x What is the equation of the tangent line at P(5,f(5)). The slope of the tangent line is 3.

Algebra ->  Graphs -> SOLUTION: Let f(x) = x^2 - 7x What is the equation of the tangent line at P(5,f(5)). The slope of the tangent line is 3.      Log On


   



Question 1046506: Let f(x) = x^2 - 7x
What is the equation of the tangent line at P(5,f(5)).
The slope of the tangent line is 3.

Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Let f(x) = x^2 - 7x
What is the equation of the tangent line at P(5,f(5)).
The slope of the tangent line is 3.
=================
Let f(x) = x^2 - 7x
f'(x) = 2x - 7
f'(5) = 3
=============
f(3) = 9 - 21 = -12 --> the point (5,-12)
---
y + 12 = 3*(x - 5)

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

if f%28x%29+=+x%5E2+-+7x, to find P(5,f%285%29), first find f%285%29
f%285%29+=+5%5E2+-+7%2A5
f%285%29+=+25+-+35
f%285%29+=+-10
so, the point is P(5,-10),
if he slope of the tangent line is m=3, equation of a line will be
y-y%5B1%5D=m%28x-x%5B1%5D%29 ...substitute m=3,x%5B1%5D=5, and y%5B1%5D=-10
y-%28-10%29=3%28x-5%29
y%2B10=3x-15
y=3x-15-10
y=3x-25