## onegirl 2 years ago Find the linear approximation to f(x) at x = x o. Graph the function and its linear approximation. f(x) = sin 3x, x 0, = 0

1. onegirl

2. satellite73

this is the same as "find the equation of the line tangent to the graph of $$y=\sin(3x)$$ at $$(0,0)$$"

3. satellite73

take the derivative, replace $$x$$ by 0 for the slope (you will get 3) and then use the point slope formula

4. satellite73

since the point is $$(0,0)$$ the equation of the line will be $$y=3x$$

5. onegirl

ok so find the derivative of sin 3x right?

6. satellite73

yes

7. onegirl

Ok so i got 3cos(3x)

8. satellite73

yes now evaluate at $$x=0$$ to find your slope

9. onegirl

ok i got 3

10. satellite73

yes

11. satellite73

that is the slope of your line

12. onegirl

okay so now i have to use the point slop formula?

13. satellite73

yes

14. satellite73

but the point is $$(0,0)$$ so it is just $$y=3x$$

15. onegirl

okay so what do i do next?

16. satellite73

you are done

17. onegirl

okay

18. electrokid

linear approximation of f(x) at x=x0: $f(x)=f(x_0)+(x-x_0)f'(x_0)$

19. electrokid

you can use this way too. (notice the resemblance to equation of line)