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Math Help - Can someone please check my homework?

  1. #1
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    Can someone please check my homework?

    Hi could one of the geniuses out there please check my homework?

    Find the stationary points for f(x)=-2x^3+27x^2-84x+32
    =-2(3x^2)+27(2x)-84(1)
    =-6(x^2-9x+14)
    =-6(x-2) (x-7)
    Stationary points x=2 x=7

    Then classify the left hand side using the First Derivative Test
    x=2 xl=1 xr=3
    f'(1)=-6(1) (-32) =190 >0
    f'(3)= -6 (3) (-32) =-576 <0
    So f has a local minimum at x=2

    Classify the right hand side using the Second Derivative Test
    x=7
    Second derivative
    -6(2x) + 54
    =-12x + 54
    =-6(2x - 9)
    For stationary point x=7 xl=6 xr=8
    f"(6) =-6((2x6)-(9x6))=252>0
    f"(8) = -6((2x8)-(9x8)=336>0

    Find the y coordinates x=2 x=7
    f(2)= -16+1458-168+32=1306
    f(7)=-56+5103-588+32 = 4491

    I know theres a lot but would be greatful for any help.
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  2. #2
    Super Member

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    Hello, stewpot!

    I don't understand the procedure you're using . . .
    . . First Derivative Test for the "left side"?
    . . Second Derivative Test for the "right side"?

    Who told you to do it that way ??


    Find and identify the stationary points for: . f(x)\:=\:-2x^3+27x^2-84x+32
    Set the first derivative equal to zero: . f'(x) \:=\:-6x^2 + 54x - 84 \:=\:0

    . . which factors:. . -6(x - 2)(x - 7) \:=\:0

    . . and has roots: . x \:=\:2,\:7

    Stationary points: . (2,\text{-}44),\;(7,81)


    Second Derivative Test: . f''(x) \:=\:-12x + 54 \:=\:-6(2x-9)

    . . f''(2) \:=\:-6(4-9) \:=\:+30\;\hdots\text{ concave up: }\cup\;\hdots\text{ minimum at }(2,\text{-}44)

    . . f''(7) \:=\:-6(14-9) \:=\:\text{-}30\;\hdots\text{ concave down: }\cap\;\hdots\text{ maximum at }(7,81)

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  3. #3
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    Near London
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    Can you please show me how you arrived at this!

    H Soroban,

    Thanks for you speedy answer, I'm a little puzzled, can you break down how you arrived at the coordinates from [IMG]file:///Users/andystewart/Library/Caches/TemporaryItems/moz-screenshot.jpg[/IMG]-6(x-2)(x-7)=0.

    I've tried most solutions and keep comming up with different coordinates!

    Many thanks

    Stewpot
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