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 =??
y =??

  1. 👍 0
  2. 👎 0
  3. 👁 473
  1. 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

    1. 👍 0
    2. 👎 1

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    An equation of the line tangent to the graph of y=(2x+3)/(3x-2) at the point (1,5) is...do I take the derivative of y=(2x+3)/(3x-2) to find the slope and then plug that into y-5=m(x-1)?

  2. calculus

    5. Let f be the function given by f(x) = x3- 7x + 6. a. Find the zeros of f b. Write an equation of the line tangent to the graph of f at x = -1 c. Find the x coordinate of the point where the tangent line is parallel to the

  3. Calculus - Functions?

    #1. A cubic polynomial function f is defined by f(x) = 4x^3 +ax^2 + bx + k where a, b and k are constants. The function f has a local minimum at x = -1, and the graph of f has a point of inflection at x= -2 a.) Find the values of

  4. Calculus

    1. use the definition mtan=(f(x)-f(x))/(x-a) to find the SLOPE of the line tangent to the graph of f at P. 2. Determine an equation of the tangent line at P. 3. Given 1 & 2, how would I plot the graph of f and the tangent line at

  1. 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 = ?? y = ?? .

  2. calculus

    The point P(7, −4) lies on the curve y = 4/(6 − x). (a) If Q is the point (x, 4/(6 − x)), use your calculator to find the slope mPQ of the secant line PQ (correct to six decimal places) for the following values of x. (i) 6.9

  3. Algebra

    graph the equation x-3=y (where do I plot the points?) find the intercepts and then graph: 5x+4y=20 find the intercepts and then graph: 1.4x-1.3y=3.64 graph the equation using slope and y-intercept: y=10/7x +4 graph using slope

  4. Math

    Consider the graph of the parabola ​f(x)equals=x squaredx2. For xgreater than>0 and hgreater than>​0, the secant line through​ (x,f(x)) and ​(xplus+​h,f(x+h)) always has a greater slope than the tangent line at​

  1. Math

    1. Graph the points A ( -5,0) B ( -4, 3) and C ( 0, -4) A B C D 2. Identify the quadrant in which (3, -6) lies A II B IV C I D III 3. Determine which ordered pair is a solution of y = 2x - 3 A ( -2, 7) B ( 0, 3) C ( -4, -11 D ( 5,

  2. I would like to understand my calc homework:/

    Consider the differential equation given by dy/dx=(xy)/(2) A) sketch a slope field (I already did this) B) let f be the function that satisfies the given fifferential equation for the tangent line to the curve y=f(x) through the

  3. Calculus

    1. a) For the Function and point below , Find f’(a). b) Determine the equation of the line tangent to the graph of f at (a,f(a)) for the given value of f(x) = 4x2+2x, a =1 F’(a) = y = 2. For the function find f’ using the

  4. Math (Secant Lines)

    Consider the function f(x)=sqrt(x) and the point P(4,2) on the graph of f? -Consider the graph f with secant lines passing through p(4,2) and Q(x,f(x)) for x-values 1, 3, and 5. -Find the slope of each secant line -Use the results

You can view more similar questions or ask a new question.