calculus

posted by .

Consider a differentiable functionf having domain all positive real numbers, and for which it is known that f'(x)=(4-x)^-3 for x.0
a. find the x-coordinate of the critical point f. DEtermine whether the point is a relative maximum or minomum, or neither for the fxn f. justify your answer.
b) find all intervals on which the graph of f is concave down. jusity answer.
c. given that f(1)=2 determine the fxn f.
i got a but how do you do b and c?

  • calculus -

    c)
    if f'(x) = (4-x)^-3
    then f(x) = (1/2)(4-x)^-2 + c
    given f(1) = 2
    2 = (1/2)(4-1)^-2 + c
    2 = (1/2)(1/9) + c
    c = 2 - 1/18 = 35/18

    f(x) = (1/2)(4-x)^-2 + 35/18

    f''(x) = -3(4-x)^-4 (-1) = 3/(4-x)^4

    the graph is concave up when f''(x) > 0
    the graph is concave down when f''(x) < 0

    since (4-x)^4 is always positive, for x≠4
    then 3/(4-x)^4 is always positive.
    So the curve is concave up for all x's in the domain.

    here is what Wolfram thinks of your function
    http://www.wolframalpha.com/input/?i=%281%2F2%29%284-x%29%5E-2+%2B+35%2F18

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calc

    let f be function given by f(x)= Ln(x)/x for all x> 0. the dervative of f is given by f'(x)= (1 - Ln(x))/x squared. a) write equation for the line tangent to the graph of f at x=e squared b) Find the x-coordinate of the critical …
  2. Calc

    Let f be the function given by f(x)=2ln(x^2+3)-x with domain -3 is less than or equal to x which is less than or equal to 5 a) Find the x-coordinate of each relative maximum point and each relative minimum point of f. Justify your …
  3. Calculus

    Use the given derivative to find all critical points of 'f' and at each critical point determine whether a relative maximum, relative minimum, or neither occurs. Assume that 'f' is continuous everywhere. f' (x) = (1-2x)/ ∛(x+3) …
  4. Calculus

    Use the given derivative to find all critical points of 'f' and at each critical point determine whether a relative maximum, relative minimum, or neither occurs. Assume that 'f' is continuous everywhere. f' (x) = (1-2x)/ ∛(x+3)
  5. calculus

    If g is a differentiable function such that g(x) is less than 0 for all real numbers x and if f'(x)=(x2-4)g(x), which of the following is true?
  6. calculus

    Consider a differentiable functionf having domain all positive real numbers, and for which it is known that f'(x)=(4-x)^-3 for x.0 a. find the x-coordinate of the critical point f. DEtermine whether the point is a relative maximum …
  7. Calculus

    Let g and h be any two twice-differentiable functions that are defined for all real numbers and that satisfy the following properties for all x: I) (g(x))^2 + (h(x))^2=1 ii) g'(x)= (h(x))^2 iii) h(x)>0 iv) g(0)=0 a)Justify that …
  8. calculus

    I needed help with these FRQ in my APCalc course. Any help or walkthrough would be extremely helpful - thanks in advance. Let f be the function given by f(x)=3ln((x^2)+2)-2x with the domain [-2,4]. (a) Find the coordinate of each relative …
  9. Please check my Calculus

    1. Which of the following describes the behavior of f(x)=x^3-x A. Relative maximum: x=0 B. Relative maximum: x=(1/sqrt(3)); Relative minimum: x=(-1/sqrt(3)) C. Relative maximum: x=(-1/sqrt(3)); Relative minimum: x=(1/sqrt(3)) D. Relative …
  10. Calculus

    Consider a differentiable function f having domain all positive real numbers, and for which it is known that f'(x)=(4-x)x^-3 for x>0. A. Find the x-coordinate of the critical point of f. Determine whether the point is a relative …

More Similar Questions