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Math Help - Find Maxima Minima Of A Function

  1. #1
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    Find Maxima Minima Of A Function

    For the following function, find a point of maxima and a point of minima, if these exist

    f(x) = 12x6 4x4 + 15x3 1.
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    Senior Member topher0805's Avatar
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    f(x) = 12x^6-4x^4+15x^3-1

    First, find the derivative of the function:

    f'(x) = 72x^5-16x^3+45x^2

    Now find the critical points. These occur when the derivative function is equal to zero or when it is undefined. Since the function is never undefined, the critical points occur only when it is equal to 0.

    So, find the critical points. Then, create a sign chart. Where the sign changes from positive to negative you have a maximum and where it changes from negative to positive you have a minimum.
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  3. #3
    Moo
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    Hello,

    Firstly, derivate the function.

    f'(x)=72x^5-16x^3+45x^2=x^2(72x^3-16x+45)

    0 annulates the derivative twice. But it's not a maxima or minima. Take a look at "inflexion point"

    Now i'm afraid you will have to derivate 72x^3-16x to get its variations of sign.

    Then, make a sign table of the derivative of f and find its maxima and minima (it's quite hard to write it down on a computer...)
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by rajdey1 View Post
    For the following function, find a point of maxima and a point of minima, if these exist

    f(x) = 12x6 4x4 + 15x3 1.
    find f'(x) and f''(x)

    critical points occur when f'(x) = 0 or is undefined. find all such points.

    when you get the points, plug them into the second derivative f''(x)

    if f''(x) < 0 at the point, then we have a maximum

    if f''(x) > 0 at the point, then we have a minimum
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  5. #5
    Behold, the power of SARDINES!
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    Quote Originally Posted by rajdey1 View Post
    For the following function, find a point of maxima and a point of minima, if these exist

    f(x) = 12x6 4x4 + 15x3 1.
    if you use math and /math in [] and this code you will get the function below.
    f(x)=12x^6-4x^4+15x^3-1

    I asuume you mean

    f(x)=12x^6-4x^4+15x^3-1

    \frac{df}{dx}=72x^5-16x^3+45x^2=x^2(72x^3-16x+45)

    now lets focus on

    g(x)=72x^3-16x+45

    well

     g(-1)=-72+16+45=-11 \mbox{ and }g(0)=45

    so we know that it has at least one real root inbetwwen -1 and 0

    if it is rational you can use the rational roots theorem, if not try numerical methods.

    I hope this will get you started. Good luck.
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  6. #6
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    Quote Originally Posted by Moo View Post
    hello,

    Please take a look at your previous topics... I think that 4 people have answered you
    ya but please help me to move forward with the problem after frist derivative test i have been unable to locate the critical points
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  7. #7
    MHF Contributor Mathstud28's Avatar
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    I will give you a hint

    Quote Originally Posted by rajdey1 View Post
    For the following function, find a point of maxima and a point of minima, if these exist

    f(x) = 12x6 – 4x4 + 15x3 –1.


    please help to find all the critical point of the function i am finding it difficult to solve the problem after doing frist derivative test

    f'(x)=72x^5-16x^3+15x^2...here is your hint f'(-1)=-11 and f'\bigg(\frac{-1}{2}\bigg)=-11
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