SOLUTION: Again, I know there is not a section, but can anyone help with the following problem please? Find the equation of the tangent line to the curve when x has the given value. f(x)

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Again, I know there is not a section, but can anyone help with the following problem please? Find the equation of the tangent line to the curve when x has the given value. f(x)      Log On


   

Question 441548: Again, I know there is not a section, but can anyone help with the following problem please?
Find the equation of the tangent line to the curve when x has the given value.
f(x) = x2 + 5x ; x = 4
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+f%28x%29+=+x2+%2B+5x+
The derivative equation is
+d1%28x%29+=+2x+%2B+5+
+d1%284%29+=+2%2A4+%2B+5+
+d1%284%29+=+13+
and
+f%284%29+=+4%5E2+%2B+5%2A4+
+f%284%29+=+16+%2B+20+
+f%284%29+=+36+
Now I have a point, (4,36)
and the slope +m+=+13+
+y+=+mx+%2B+b+
+y+=+13x+%2B+b+
+36+=+13%2A4+%2B+b+
+36+=+52+%2B+b+
+b+=+-16+
The equation of the tangent is
+y+=+13x+-+16+
Here's the plot:
+graph%28+500%2C+500%2C+-10%2C+6%2C+-8%2C+44%2C+13x+-+16%2C+x%5E2+%2B+5x+%29+