question :)

izzy_xo · 2 Nov 2009, 3:41 PM

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i can't work out this question :|

The tangent to the curve y=ax^3+2 at the point where x=3 is inclined at 135degrees to the x-axis. Find the value of a.

Any help would be greatly appreciated

Uncle · 2 Nov 2009, 4:00 PM

I worked out this problem in 3 seconds but hopefully it should be the case.

Definition of the gradient function, derivative, slope, etc. same thing.

$m = \frac{\mathrm{dy} }{\mathrm{d} x} = tan \theta$

y = ax³ + 2

$\frac{\mathrm{dy} }{\mathrm{d} x} = 3ax^{2}$

Given x = 3 and $\theta$ = 135⁰

3a(3)² = tan 135⁰

$a = \frac{tan 135^{\circ}}{27}$

izzy_xo · 2 Nov 2009, 4:03 PM

hey thanks,
but the answers in the book say a=-1/27
hmm

Uncle · 2 Nov 2009, 4:24 PM

Quote:

Originally Posted by izzy_xo

hey thanks,
but the answers in the book say a=-1/27
hmm

Just found a calculator.
tan 135⁰ = -1

o rly?

YAY!

izzy_xo · 2 Nov 2009, 4:35 PM

hahahaaha thankss
clearly can't think straight today

2 Nov 2009, 3:41 PM	#1 (permalink)
izzy_xo New Member HSC: 2010 Gender: Female Join Date: Apr 2009 Posts: 24 Last Activity: Today, 5:21 PM	question :) You can hide this advertisement by registering. i can't work out this question :\| The tangent to the curve y=ax^3+2 at the point where x=3 is inclined at 135degrees to the x-axis. Find the value of a. Any help would be greatly appreciated

2 Nov 2009, 4:00 PM	#2 (permalink)
Uncle Ninjaneer HSC: 2007 Gender: Male Location: Retirement Village of Alaska Join Date: Feb 2009 Posts: 3,211 Last Activity: Yesterday, 12:05 PM Blog Entries: 20	Re: question :) I worked out this problem in 3 seconds but hopefully it should be the case. Definition of the gradient function, derivative, slope, etc. same thing. $m = \frac{\mathrm{dy} }{\mathrm{d} x} = tan \theta$ y = ax³ + 2 $\frac{\mathrm{dy} }{\mathrm{d} x} = 3ax^{2}$ Given x = 3 and $\theta$ = 135⁰ 3a(3)² = tan 135⁰ $a = \frac{tan 135^{\circ}}{27}$ __________________ .

2 Nov 2009, 4:03 PM	#3 (permalink)
izzy_xo New Member HSC: 2010 Gender: Female Join Date: Apr 2009 Posts: 24 Last Activity: Today, 5:21 PM	Re: question :) hey thanks, but the answers in the book say a=-1/27 hmm

2 Nov 2009, 4:35 PM	#5 (permalink)
izzy_xo New Member HSC: 2010 Gender: Female Join Date: Apr 2009 Posts: 24 Last Activity: Today, 5:21 PM	Re: question :) hahahaaha thankss clearly can't think straight today

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