## anonymous 2 years ago How to solve this? A curve has an equation y=2/x^2 + 5/2 Find the equation of the tangent to the curve at point (2,3)

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1. anonymous

$\frac{ 2 }{x ^{2} }+\frac{ 5 }{ 2 }$

2. anonymous

what did u just wrote, it became error. all of a sudden

3. anonymous

is that the equation

4. anonymous

do you need to take the derivative

5. anonymous

|dw:1384947669567:dw|

6. anonymous

is the equation, right?

7. anonymous

@Peter14 yes that is the equation

8. anonymous

@Decart yes,need to take the derivative , how?

9. anonymous

quotient rule

10. anonymous

i get dy/dx = -4x^-3, after that what should i do?

11. anonymous

or simplify it to 2x^(-2)

12. anonymous

the low times the derivative of the high - the high times the derivative of the low all divided by the low squared

13. anonymous

do you know point-slope form?

14. anonymous

no

15. anonymous

once you find the derivative that gives you the slope

16. anonymous

the derivative is $\frac{ 4 }{ x ^{3} }$

17. anonymous

plug in the x to get the slope

18. anonymous

with a point (x1, y1) and a slope m the equation of a line can be written (y-y1)=m(x-x1)

19. anonymous

1/2 is m ?

20. anonymous

yes

21. anonymous

y-3=1/2(x-2)

22. anonymous

distribute the 1/2 and then add the three

23. anonymous

i got it!!! i have another question

24. anonymous

solve the equation 3 cos 2x + 5 sinx =4 for 0 <x<360

25. anonymous

you have to simplify it first, use the identity for cos 2x

26. anonymous

how to simplify that?

27. anonymous

use the identity for cos 2x