Question

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

Answer 1

differentiate each and equate the derivatives

Answer 2

x=1/4

Answer 3

woah @akash123 where'd that come from?

Answer 4

differentiate each and equate the derivatives

Answer 5

:)

Answer 6

You were scaring me there

Answer 7

@JJ1371 taking it in...

Answer 8

where? proving the collinearity..

Answer 9

no, just suddenly pulling an answer

Answer 10

oh...ok

Answer 11

sorry, the second y=x^3

Answer 12

Ok, follow the procedure

Answer 13

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

Answer 14

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

Answer 15

1+2x = 3x^2

Answer 16

okay
2x^2-2x-1=0

Answer 17

derivative of x^3 = 3 x^2

Answer 18

how did you get that?

Answer 19

derivative of x^n = n x^(n-1)

Answer 20

oh right yeah

Answer 21

sorry

Answer 22

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

Answer 23

wait!
(x-3)(x+1) = 0

Answer 24

therefore x = 3 or x = -1?

Answer 25

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

Answer 26

damn

Answer 27

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

Answer 28

yes?

Answer 29

yes...:)