1. Questions

calculus

Use analytic methods to find the global extreme values of the function on the interval and state where they occur.

y=x(2-x)^(1/2), -2<=x<=2

  1. 👍
  2. 👎
  3. 👁
Jocelyn

  1. Find the first derivative of the function:
    dy/dx = (2-x)^(1/2) - (1/2)x.(2-x)^(-1/2)
    = (4-3x)/2sqrt(2-x)

    You have to be careful in this matter, especially since you've encountered a square root form in the denominator.
    * take the denominator, ignore the constant in front of the square root. We know that the original rule for square root that to have a non-imaginary result, the value under the root should be >= 0. However, since this form is in the denominator, the rule now becomes > 0. So:
    2 - x > 0
    x < 2
    * now take the nominator. Since the denominator value will always be positive, nominator value will be the 'decision maker', whether the graph function is increasing or decreasing.
    4 - 3x = 0
    x = 4/3
    To find the global extreme values, just substitute this value to the original equation to find y
    As for the behaviour, test one condition. Say that you want to know when the graph of this function is increasing
    4 - 3x > 0
    x < 4/3
    So, we can say that the function is increasing at interval [-2,4/3) or -2<=x<4/3, and decreasing at the interval (4/3,2) or 4/3<x<2

    1. 👍
    2. 👎
    agrin04

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    Let f be the function with f(0) = 1/ (pi)^2, f(2) = 1/(pi)^2, and the derivative given by f'(x) = (x+1)cos ((pi)(x)). How many values of x in the open interval (0, 2) satisfy the conclusion of the Mean Value Theorem for the

  2. Calculus

    1. The function is continuous on the interval [10, 20] with some of its values given in the table above. Estimate the average value of the function with a Left Hand Sum Approximation, using the intervals between those given

  3. Calculus

    1. Locate the absolute extrema of the function f(x)=cos(pi*x) on the closed interval [0,1/2]. 2. Determine whether Rolle's Theorem applied to the function f(x)=x^2+6x+8 on the closed interval[-4,-2]. If Rolle's Theorem can be

  4. Math

    Find the intervals on which the function is increasing, decreasing, concave up, or concave down and find any local extreme values and inflection points. So I know how to do the above, but not with piece wise functions. Someone

  1. calculus

    Find the values of c that satisfy the Mean Value Theorem for f(x)=6/x-3 on the interval [-1,2]. Is it no value of c in that interval because the function is not continuous on that interval???

  2. Math

    Find the average value of the function over the given interval and all values of x in the interval for which the function equals its average value. f(x) = 4x3 − 3x2, [−1, 2]

  3. calculus

    1. Find the average value have of the function h on the given interval. h(x) = 2 cos4(x) sin(x), [0, π] 2. Consider the given function and the given interval. f(x) = 6 sin(x) − 3 sin(2x), [0, π] (a) Find the average value fave

  4. grade 12 AP calculus

    for f(x= -1/4x4-1/3x3+2x, use analytic method to find the exact intervals on which the function is a)increasing, b)decreasing, c)concave up, d)concave down, then find any e)local extreme values, f)inflection points

  1. Calculus

    Consider the function f(x) = 5/4x^4 + 2/3x^3 - 5x^2 - 4x + 5 a. Find any relative extrema for f(x); be sure to label each as a maximum or minimum. You do not need to find function values; just find the x-values. b. Determine the

  2. Math

    Use graphing utility to graph function and estimate the limit. Use a table to reinforce your conclusion. Then find the limit by analytic methods. lim (sq root of (x+2) - sq root of 2) / x x->0 Thanks!

  3. Algebra 1

    Question 9 Examine the graph of f(x) f ( x ) and the table that contains values of g(x). g ( x ) . Curve f of x approaches Y equals negative 7 on the left and positive infinity on the right. It passes through points (0, negative

  4. Calculus

    Consider the function f(x)=sin(5x)/x. (a) Fill in the following table of values for f(x): x= -0.1 -0.01 -0.001 -0.0001 0.0001 0.001 0.01 0.1 f(x)= ( I need the values of f(x) for each x) (b) Based on your table of values, what

You can view more similar questions or ask a new question.