Calc

posted by .

The function f is defined by f(x)= (25-x^2)^(1/2) for -5 less than or = x less than or = 5
A) find f'(x)
B) write an equation for the tangent to the graph of f at x=3
C) let g be the function defined by g(x)= (f(x) for -5<or=x<or=-3)and (x+7 for -3<or=x<or=5)
D) find the value of the intagral 5 over 0 of x(25-x^2)^(1/2)dx

  • Calc -

    do you have no idea at all about any of these questions? Hard to believe this would come up till the topics have been covered. They look like pretty straightforward calculus and algebra operations.

    How far do you get?

  • Calc -

    i found A and B, just checking if they're right. C i can never remember how to do these. D i haven't tried yet but i could probably figure out but i figured since i was putting the rest up i would do it as well

  • Calc -

    There's nothing to figure out for C. They're just defining a new function. Not sure why it's even there.

    For D, it's pretty straightforward. Let
    u = 25-x^2
    then du = -2x dx and we have

    ∫[0,5] x√(25-x^2) dx
    = ∫[5,0] -1/2 √u du
    and it's clear sailing from there on

  • Calc -

    thank youu

  • Calc -

    A: d/dx √(25-x^2) = -x/√(25-x^2)

    B. At x=3, f(x)=4, so
    f'(3) = -3/4
    Now you have a point (3,4) and a slope: -3/4
    y-4 = -3/4 (x-3)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 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 a …
  2. calculous

    3.Given the function f defined by f(x)=2x^3-3x^2-12x+20 a.Find the zeros of f b.Write an equation of the line perpendicular to the graph of f at x = 0 c. Find the x and y coordinates of all points on the graph of f where the line tangent …
  3. Calculus

    Given the function defined as f(x)=x^3-(3/2)x^2-6x+10 a) Explain why f(x) must have a root between x=-3 and x=-2 b) Write an equation of the line perpendicular to the graph of f at x=0 c) Find the x and y coordinates of the point on …
  4. Calculus

    1. Given the function f defined by f(x) = x^3-x^2-4X+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) …
  5. Calc

    Write the equation of the line tangent to the graph of the function at the indicated point. As a check, graph both the function and the tangent line you found to see whether it looks correct. (1/x^3 -x)^2 at x= 2
  6. Calculus c

    Let f be a twice-differentiable function defined on the interval -1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the x-axis at …
  7. Calculus

    Let f be a twice-differentiable function defined on the interval -1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the x-axis at …
  8. Clueless in calculus

    The function f is defined by f(x)= (25-x^2)^(1/2) for -5 less than or = x less than or = 5 A) find f'(x) B) write an equation for the tangent to the graph of f at x=3 C) let g be the function defined by g(x)= (f(x) for -5<or=x<or=-3)and …
  9. Calculus

    The function g is defined for x>0 with g(1)=2, g'(x)=sin(x+1/x), and g"(x)=(1-1/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 …
  10. math, a.p. calc

    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. Write an equation for the tangent line to the graph of g at the point where x …

More Similar Questions