## JJ1371 3 years ago For what value of x does y=x-x^2 and y=x^2 have the same gradient?

1. apple_pi

differentiate each and equate the derivatives

2. akash123

x=1/4

3. apple_pi

woah @akash123 where'd that come from?

4. akash123

differentiate each and equate the derivatives

5. akash123

:)

6. apple_pi

You were scaring me there

7. apple_pi

@JJ1371 taking it in...

8. akash123

where? proving the collinearity..

9. apple_pi

no, just suddenly pulling an answer

10. akash123

oh...ok

11. JJ1371

sorry, the second y=x^3

12. apple_pi

13. JJ1371

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

14. akash123

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

15. akash123

1+2x = 3x^2

16. JJ1371

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

17. akash123

derivative of x^3 = 3 x^2

18. JJ1371

how did you get that?

19. akash123

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

20. JJ1371

oh right yeah

21. JJ1371

sorry

22. JJ1371

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

23. JJ1371

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

24. JJ1371

therefore x = 3 or x = -1?

25. akash123

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

26. JJ1371

damn

27. JJ1371

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

28. JJ1371

yes?

29. akash123

yes...:)