JJ1371
For what value of x does y=xx^2 and y=x^2 have the same gradient?



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apple_pi
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differentiate each and equate the derivatives

akash123
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x=1/4

apple_pi
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woah @akash123 where'd that come from?

akash123
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differentiate each and equate the derivatives

akash123
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:)

apple_pi
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You were scaring me there

apple_pi
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@JJ1371 taking it in...

akash123
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where? proving the collinearity..

apple_pi
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no, just suddenly pulling an answer

akash123
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oh...ok

JJ1371
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sorry, the second y=x^3

apple_pi
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Ok, follow the procedure

JJ1371
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y=1+2x
y=2x^2
1+2x = 2x^2
where to now?

akash123
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now u have to solve this quadratic equation and find the values of x

akash123
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1+2x = 3x^2

JJ1371
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okay
2x^22x1=0

akash123
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derivative of x^3 = 3 x^2

JJ1371
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how did you get that?

akash123
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derivative of x^n = n x^(n1)

JJ1371
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oh right yeah

JJ1371
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sorry

JJ1371
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3x^2  2x 1 = 0
Quadratic equation?

JJ1371
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wait!
(x3)(x+1) = 0

JJ1371
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therefore x = 3 or x = 1?

akash123
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no...3x^2  2x 1 = 0 =(x3)(x+1) is wrong
do the factorization again

JJ1371
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damn

JJ1371
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x = 1
or
x=(1/3)

JJ1371
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yes?

akash123
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yes...:)