calculus
posted by fareha .
1. Let y = f(x) be the continuous function that satisfies the equation x^45x^2y^2+4y^4=0 and whose graph contains the points (2, 1) and (2, 2). Let l be the line tangent to the graph of f at x = 2.
a. Find an expression for y’
b. Write an equation for line l

differentiate implicitly:
4x^3  10xy^2  10x^2yy' + 16y^3y' = 0
y'(16y^3  10x^2y) = 10xy^2  4x^3
y' = x(5y^2  2x^2) / y(8y^2  5x^2)

y'(2) = 2(58) / (820) = 6/12 = 1/2
Line l is (y1)/(x2) = 1/2
Respond to this Question
Similar Questions

Calculus
55. Find an equation of the tangent line to the graph of f(x) =x^3  2x + 1 a) at (2,5); b) at (1,2); c) at (0,1). I believe the answers are: a) y= (3/2 x)  (3/2) b) No solution c) No solution For each function, find the points on … 
MathCalculus
Let y = f(x) be the continuous function that satisfies the equation x^4  (5x^2)(y^2) + 4y^4 = 0 and whose graph contains the points (2,1) and (2,2). Let L be the line tangent to the graph of f at x = 2. (a) Find and expression for … 
calculus
find the equation of a quadratic function whose graph is tangent at x=1 to the line whose slope8, tangent at x=2 to solve the line with slope4 and tangent to the line y=8 
cal
find the equation of a quadratic function whose graph is tangent at x=1 to the line whose slope8, tangent at x=2 to solve the line with slope4 and tangent to the line y=8 find the equation of the tangent lines at x=1 and x=2 graph … 
calculus
1. Let y = f(x) be the continuous function that satisfies the equation x^45x^2y^2+4y^4=0 and whose graph contains the points (2, 1) and (2, 2). Let l be the line tangent to the graph of f at x = 2. a. Find an expression for y’ … 
Calculus
1. Given the function f defined by f(x) = x^3x^24X+4 a. Find the zeros of f b. Write an equation of the line tangent to the graph of f at x = 1 c. The point (a, b) is on the graph of f and the line tangent to the graph at (a, b) … 
Calculus
Given the function y=(x^25/x+3), answer the following questions. a) Find dy/dx. Simplify your answer b) Find the coordinates of any points on the graph of y where the tangent line is horizontal. Show your work. c) Are there any points … 
Calculus
Graph the function f(x)=x+4/x Graph the secant line that passes through the points (1,5) and (8,8.5) on the same set of axes Find the number c that satisfies the conclusion of the Mean Value Theorem for f on [1,8] c= Notice that if … 
math
This is a continuous from my last question Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g is g′(x)=(x^2–16)/(x−2) with x ≠ 2. On what intervals is the graph … 
Calculus
The function g is defined for x>0 with g(1)=2, g'(x)=sin(x+1/x), and g"(x)=(11/x^2)cos(x+1/x). A. Find all values of x in the interval 0.12<=x<=1 at which the graph of g has a horizontal tangent line. B. On what subintervals …