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HSC Stuff => HSC Maths Stuff => HSC Subjects + Help => HSC Mathematics Extension 1 => Topic started by: hanaacdr on January 13, 2017, 11:50:23 am

Title: Maxima minima questions
Post by: hanaacdr on January 13, 2017, 11:50:23 am

hi
can i please get some help on these two questions

1. find the values of x for which the curve y= 2x^3-3x^2-12x+6 rises with downward concavity

2. is in the attachment

thanks

Title: Re: Maxima minima questions
Post by: hanaacdr on January 13, 2017, 12:01:41 pm

hi could i also get some help with question as well
thank you

Title: Re: Maxima minima questions
Post by: RuiAce on January 13, 2017, 12:16:04 pm

Quote from: hanaacdr on January 13, 2017, 11:50:23 am

hi
can i please get some help on these two questions

1. find the values of x for which the curve y= 2x^3-3x^2-12x+6 rises with downward concavity

2. is in the attachment

thanks

1. y' = 6x^2 - 6x - 12
y" = 12x - 6

You want to solve y' > 0 for the 'rises' part
AND y" < 0 for the downward concavity part.
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2.

xy = 10000 because the area is 10000
So y = 10000/x

Fencing is just the perimeter of the rectangle, PLUS the arc length of the 1/4 of a circle (which is the pi.x/4 part)

And then it's your classic maxima/minima question. dL/dx = 4 + pi/2 - 10000/x^2
so set dL/dx = 0, and do your usual thing
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For the other one, you're not gonna get anywhere if you don't draw a diagram.
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Post any working out you have if you are stuck on any of them as you progress.