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Higher Further Calculus and Stationary Point Help? watch

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    Doing a past paper, came across this question:


    "A function f is defined by f(x)=(2x-1)^5

    Find the coordinates of the stationary point on the graph with equation y=f(x) and determine it's nature"

    So far I've differentiated f(x) to 10(2x-1)^4, then equated it to zero for Stationary Points.

    Where do I go from there? How do I find the x coordinate? I know how to do stationary points normally, but not like this.
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    (Original post by FloatinHeadDr)
    Doing a past paper, came across this question:


    "A function f is defined by f(x)=(2x-1)^5

    Find the coordinates of the stationary point on the graph with equation y=f(x) and determine it's nature"

    So far I've differentiated f(x) to 10(2x-1)^4, then equated it to zero for Stationary Points.

    Where do I go from there? How do I find the x coordinate? I know how to do stationary points normally, but not like this.
    Well if \frac{dy}{dx} = 10(2x-1)^4 and you equate that to 0, then divide through by 10 you end up with  (2x-1)^4 = 0 . Now what must 2x-1 be equal to if when it is raised to the power of four it is equal to zero? Remember, it's 4 identical things multipled together, and when you multiply 2 numbers together and get zero what must at least one of the numbers be equal to?
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    (Original post by FloatinHeadDr)
    Doing a past paper, came across this question:


    "A function f is defined by f(x)=(2x-1)^5

    Find the coordinates of the stationary point on the graph with equation y=f(x) and determine it's nature"

    So far I've differentiated f(x) to 10(2x-1)^4, then equated it to zero for Stationary Points.

    Where do I go from there? How do I find the x coordinate? I know how to do stationary points normally, but not like this.
    f(x)=(2x-1)^5
    f'(x)=10(2x-1)^4
    f'(x)=0
    10(2x-1)^4=0
    (2x-1)^4=0
    (2x-1)=0
    2x=1
    x=1/2
    when f'(x)>0, it is a minimum point. when f'(x)<0, it is a maximum point
    In this case 1/2>0, so its nature is a minimum.
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    I now feel like a complete idiot.

    Derp.
 
 
 
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