## onegirl Group Title 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 one year ago one year ago

1. onegirl Group Title

2. satellite73 Group Title

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

3. satellite73 Group Title

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

4. satellite73 Group Title

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

5. onegirl Group Title

ok so find the derivative of sin 3x right?

6. satellite73 Group Title

yes

7. onegirl Group Title

Ok so i got 3cos(3x)

8. satellite73 Group Title

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

9. onegirl Group Title

ok i got 3

10. satellite73 Group Title

yes

11. satellite73 Group Title

that is the slope of your line

12. onegirl Group Title

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

13. satellite73 Group Title

yes

14. satellite73 Group Title

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

15. onegirl Group Title

okay so what do i do next?

16. satellite73 Group Title

you are done

17. onegirl Group Title

okay

18. electrokid Group Title

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

19. electrokid Group Title

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