Find the maximum of f(x)=2+5x−x^2?

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  • Como
    Lv 7
    4 weeks ago

    :-

    f ' (x) = 5 - 2x = 0 for turning point

    x = 5/2

    f (5/2) = 2 + 25/2 - 25/4 = 2 + 25/4 = 33/4

    Turning point (5/2 , 33/4)

    f ' ' ( x ) = - 2 < 0 thus is a maximum turning point.

  • 4 weeks ago

    f '(x) = 5 - 2x

    0 = 5 - 2x

    2x = 5

    x = 5/2

    f ''(x) = -10 < 0 so we know a maximum occurs at x = 5/2.

    f(1/2) = 2 + 5(5/2) - (5/2)^2 = 2 + 25/2 - 25/4 = 8/4 + 50/4 - 25/4 = 33/4

  • MyRank
    Lv 6
    4 weeks ago

    f(x) = 2 + 5x - x²

    2 + 5x - x² = 0x = -5 ± √25 - 4.2(-1) / 2 . -1= -5 ± √25 + 8 / -2= -5 ± √33 / -2f’(x) = 0 + 5.1 - 2x= 5 - 2xf’(x) = 05 - 2x = 0x = 5/2f(x) > 0 minimum valuef(x) < 0 maximum value.

  • 4 weeks ago

    The maximum of f(x) = 2 + 5x − x^2 or -x^2 + 5x + 2

    Since this is a parabolic equation and the value of #a < 0#

    it opens downwards so it has an absolute maxima.

    The maximum point is determined by #x_(max) = -b/(2a)#

    where b and a are coefficients.

    -5/-2 = 2.5

    sub x = 2.5 back into equation to get y = 8.25

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  • 4 weeks ago

    without calculus, first write it in Standard Form:

    f(x)=−x^2 +5x +2 is the equation in the correct 'form'

    From the Quadratic Equation: use -b/2a  ±√(b² -4ac)/2a

    x = -b/2a = -(5)/(2*-1) = 5/2

    sub x=5/2 back into equation to get y=8.25

    With calculus: take 1st derivative = 0, that's where slope =0, for the minimum or maximum.  -2x +5 = 0, then x=5/2

    Attachment image
  • Vaman
    Lv 7
    4 weeks ago

    f(x)= 2+5x-x^2. To find a maximum or minimum, take fist derivative and equate that to 0. df/dx= 5- 2x. x=5/2, take the second derivative, if it is positive for x, then it is a minimum and of negative then it is a maximum. Here d^2f/dx^2=-5. The point x=5/2 is a maximum

    f= 1+25/2-25/4=27/2-25/4= (54-25)/2=29/2. This is the maximum value.

  • ted s
    Lv 7
    4 weeks ago

    IF you have studied parabola properties you should know that the vertex is when x = - b / 2a....here x = 5/2...so find f(5/2)...

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