math
posted by kim on .
Find the slope m and an equation of the tangent line to the graph of the function f at the specified point.
f(x)=x^2/x+4 ;(1,1/5)
m =??
y =??

dy/dx = slope = [ (x+4)(2x)  x^2 ] /(x+4)^2
= ( x^2 + 8 x ] / (x+4)^2
at x = 1 this slope is
= 9/25 so that is m
goes through (1, 1/5)
1/5 = (9/25)(1) + b
5/25 = 9/25 + b
b = 4/25
so
y = 9 x/25  4/25
or
25 y = 9 x  4