Question
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 ; (3,9/7)
f(x)=x^2/x+4 ; (3,9/7)
Answers
Reiny
f ' (x) = ((x+4)(2x) - 2x(1) )/(x+4)^2
= (2x^2 + 6x)/(x+4)^2
when x = 3
slope = 36/49
so y = (36/49)x + b
at (3,9/7)
9/7 = (36/49)(3) + b
b = 9/7 - 108/49
= -45/49
y = (36/49)x - 45/49 or (36x - 45)/49
check my arithmetic
= (2x^2 + 6x)/(x+4)^2
when x = 3
slope = 36/49
so y = (36/49)x + b
at (3,9/7)
9/7 = (36/49)(3) + b
b = 9/7 - 108/49
= -45/49
y = (36/49)x - 45/49 or (36x - 45)/49
check my arithmetic