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Differentiation help ,

  • Thread starter tweety1234
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  • #1
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Homework Statement



The curve [tex] y = ax^{2} + bx [/tex] passes through the point (2,4) with gradient 8. Find a and b .

I have no idea how to work out a and b , do I use simultaneous equations?

Homework Equations





The Attempt at a Solution



I have no idea how to work out a and b , do I use simultaneous equations?
 

Answers and Replies

  • #2
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well start of by thinking about what your dy/dx would be.....
 
  • #3
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okay so dy/dx = [tex] 2ax + b [/tex] from this how do I find what a and b equal ?
 
  • #4
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Use the fact that (2, 4) is a point on the curve in your given equation, which will give you an equation that involves only a and b.

Then use the fact that at x = 2, dy/dx = 8 in your equation for the derivative. This will give you another equation in a and b.

Finally, solve the two equations in a and b simultaneously.
 
  • #5
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Use the fact that (2, 4) is a point on the curve in your given equation, which will give you an equation that involves only a and b.

Then use the fact that at x = 2, dy/dx = 8 in your equation for the derivative. This will give you another equation in a and b.

Finally, solve the two equations in a and b simultaneously.
so I just sub in the values for x and y ?

are these two equations correct..

[tex] 4a + b = 4 [/tex]

[tex] 4a + b = 8 [/tex]

?
 
  • #6
danago
Gold Member
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Have another look at the first equation.
 
  • #7
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Have another look at the first equation.
x=2 so 2x2=4? can you give more hints, cause I am really stuck

thank you!
 
  • #8
112
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is it meant to be [tex] 32a + b =4 [/tex] ?
 
  • #9
33,086
4,793
is it meant to be [tex] 32a + b =4 [/tex] ?
No.

Write your first equation.
Substitute 2 for x and 4 for y in that equation. The other equation you wrote, 4a + b = 8, is correct.
 
  • #10
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[tex] y = ax^{2} + bx [/tex] , [tex] 4a + 2b = 4 [/tex] is this correct? so a = 3 and b = -4 ?
 
  • #11
HallsofIvy
Science Advisor
Homework Helper
41,770
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Check it yourself. IF a= 3 and b= -4, you have y= 3x2- 4x. What is y when x= 2? What is y' when x= 2?
 

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