Ask Question
25 December, 02:32

For what values of a, m, and b does the function f (x) satisfy the hypotheses of the mean value theorem on the interval [0 comma 3 ][0,3] ? f (x) equals=left brace Start 3 By 3 Matrix 1st Row 1st Column negative 5 2nd Column 3rd Column x equals 0 2nd Row 1st Column negative x squared plus 3 x plus a 2nd Column 3rd Column 0 less than x less than 2 3rd Row 1st Column mx plus b 2nd Column 3rd Column 2 less than or equals x less than or equals 3 EndMatrix - 5 x=0 - x2+3x+a 0

+1
Answers (1)
  1. 25 December, 05:38
    0
    a = - 5

    b = - 1

    m = - 1

    Step-by-step explanation:

    Piecewise function:

    f (x) = - 5, x=0

    f (x) = - x^2+3x+a, 0
    f (x) = mx + b 2≤x≤3

    The mean value theorem is applicable if f (x) is continuous on the entire closed interval [0; 3] and differentiable on the entire closed interval [0; 3].

    To satisfied that at x = 0:

    -x^2+3x+a = - 5

    Then, a = - 5

    Derivative of - x^2+3x-5 is - 2x + 3 and derivative of mx + b is m, at x = 2:

    -2 (2) + 3 = m

    -1 = m

    Replacing the functions at x = 2:

    -x^2+3x-5 = - x + b

    - (2) ^2+3*2-5 = - 2 + b

    -3 + 2 = b

    -1 = b
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “For what values of a, m, and b does the function f (x) satisfy the hypotheses of the mean value theorem on the interval [0 comma 3 ][0,3] ? ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers