# math

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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 =??

• math -

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

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