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Math

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find any stationary points of the function g(x) = (2x-3)square root of 5+16x-4x^2 (0 less than or equal to x less than or equal to 4) and use the first derivative test to classify each stationary point as a local maximum or local minimum of g(x)

this is how far i have got with an answer

g'(x) = (2x-3) (sqrt(5+16x-4x^2) + 2sqrt(5+16x-4x^2)

= (-4x+16)(2x-2)/sqrt(5+16x-4x^2) + 2sqrt(5+16x-4x^2)

Simplify:

-2(8x^2-30x+7) / sqrt(-4x^2+16x+5)

Set this to 0:

0 = -2(8x^2-30x+7) / sqrt(-4x^2+16x+5)


0 = -2(8x^2-30x+7)

Factor:

0 = -2(2x-7)(4x-1)

Set each factor to 0:

2x-7 = 0, so x = 7/2

4x-1 = 0, so x = 1/4

can't work out how to get the xLEFT and xRIGHT to classify each using the first derivative to get local min or local max...

help!

  • Math - ,

    Use the second derivative. It it is positive at the stationary point the function is about to get bigger so that is a minimum. If it is negative, the function is about to get smaller so that is a maximum.
    By the way I did not check what you did. I suspect it is right because you came out with reasonable points where the function is horizontal.

  • Math - ,

    call your tutor rather than trying to get someone else to do your course work for you

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