Recent content by chris40256

  1. C

    Derivatives and parallel lines

    Homework Statement Consider the curve defined by x^2+xy +y^2=27 a. Write an expression for the slope of the curve at any point (x,y) b. Determine whether the lines tangent to the curve at the x-intercepts of the curve are parallel. Show the analysis that leads to your conclusion. c...
  2. C

    AP test problems, Derivatives and Tangent lines

    Homework Statement Let f be the function given by f(x) = (2x-5)/(x^2-4). a.Find the domain of f. b.Write an equation for each vertical and each horizontal asymptote for the graph of f. c.Find f'(x). d.Write an equation for the line tangent to the graph of f at the point (0,f(0)). The...
  3. C

    Natural Log and Inverse derivatives

    Homework Statement Let f be the function given by f(x) = ln [ x/ (x-1)] (a) What is the domain of f? (b) What is the value of the derivative of f at x = -1. (c) Write an expression for f^(-1) of x, where f^(-1) denotes the inverse function of f. The Attempt at a Solution a. x / x-1...
  4. C

    AP calculus, implicit derivatives

    Homework Statement 1. Given the curve x² - xy + y² = 9 (a) Write a general expression for the slope of the curve (b) find the coordinates of the points on the curve where the tangents are vertical (c) at the point (0,3) find the rate of change in the slope of the curve with respect to x...
  5. C

    Tangent line to f(x) = -2 + ln(x²) at x = 1

    Homework Statement 1. Let f be the function defined by f(x) = -2 + ln(x^2). a) For what real numbers x is f defined b) Find the zeros of f c) Write an equation for the line tangent to the graph of f at x=1 Homework Equations The Attempt at a Solution a) all...
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