Explore BrainMass

Explore BrainMass

    Functions : Tangent, Increasing or Decreasing and Area under a Curve

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    2. Let f be a function defined on the closed interval -3≤x≤4 with f(0) = 3. The graph of f', the derivative of f, consists of one line segment and a semicircle.

    a) On what intervals, if any, is f increasing? Justify your answer.

    b) Find the x-coordinate of each point of inflection of the graph of f on the open interval -3 < x < 4. Justify your answer.

    c) Find an equation for the line tangent to the graph of f at the point (0,3).

    d) Find f(-3) and f(4). Show the work that leads to your answers.

    3. The region R, is bounded by the graphs of x = 5/3 y and the curve C given by x = (1+y^2)^(1/2), and the x-axis. The line and the curve, C, intersect at point P.

    a) Find the coordinates of point P and the value of dx/dy, yes this is typed correctly, for the curve C at point P.

    b) Set up and evaluate an integral expression with respect to y that gives the area of R.

    c) Curve C is part of the curve x^2 - y^2 = 1, Show that x^2 - y^2 = 1 can be written as the polar equation r^2 = 1/(cos^2&#952; - sin^2&#952;).

    d) Use the polar equation given in part c) to set up an integral expression with respect to theta that represents the area of R.

    © BrainMass Inc. brainmass.com March 4, 2021, 5:49 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/functions-tangent-increasing-or-decreasing-and-area-under-a-curve-12837

    Attachments

    Solution Summary

    A variety of functional property problems are solved with explanations.

    $2.49

    ADVERTISEMENT