# math

posted by .

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)

• math -

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

## Similar Questions

1. ### math

Find the slope and the equation of the tangent line to the graph of the function f at the specified point. f(x)=-10/3x^2+6x+6; (-1, -10/3) slope ?

Find the slope and the equation of the tangent line to the graph of the function f at the specified point. f(x)=-10/3x^2+6x+6; (-1, -10/3) slope ?
3. ### math

Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x)=7x-5x^2 at (-2,-34) m = ?
4. ### math

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+6;(3,1) m = ?
5. ### math

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 =?
6. ### math

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 =?
7. ### Calculus

Find the slope and the equation of the tangent line to the graph of the function f at the specified point. f(x) = -8/5 x^2 + 7 x + 7;(-1, -8/5) slope tangent line y =
8. ### Calculus derivative

find the slope m and an equation of the tangent line to the graph of the function f at the specified point. original: x^2/x+10 point: (3,9/13) After I found the derivative: (x+10)(2x)-(x^2)(1)/((x+10))^2 How do I get the slope?
9. ### calculus

1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))?
10. ### Calculus AB

Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x-1)e^x. For which value of x is the slope of the tangent line to f positive?

More Similar Questions