## anonymous one year ago explain how to find the maximum value for each function and determine which function has the largest maximum y-value.

1. anonymous

2. anonymous

@UnkleRhaukus

3. UnkleRhaukus

The function is $g(x) = 2\cos(2x-\pi)+4$ This will have maximum values when the cosine term is at maximums

4. anonymous

f(x) = −4(x − 6)^2 + 3

5. UnkleRhaukus

do you know what the largest value of $$\cos\theta$$, can ever be? (for all possible angles $$\theta$$ )

6. anonymous

no

7. UnkleRhaukus

remember that cosine is the ratio of the adjacent side in a right angled triangle, to its hypotenuse, (note that the hypotenuse is always the largest side)

8. anonymous

ok ok , i get that

9. UnkleRhaukus

|dw:1440303568385:dw|

10. UnkleRhaukus

The cosine function (like the sine function ) oscillates between its maximum and minimum values ; ±1

11. anonymous

okk

12. anonymous

So the maximun for g(x) would be 1?

13. UnkleRhaukus

not quite, that max for cos theta, and hence the max for cos(2x-π) is 1

14. UnkleRhaukus

so the max for g(x) = 2cos(2x-π) + 4 is gmax = 2(+1) + 4 =

15. anonymous

so 7 lol

16. UnkleRhaukus

(whereas the minimum is gmin = 2(-1) + 4 = -2+4 = 2 )

17. UnkleRhaukus

wait gmax = 2(+1) + 4 = 2 times 1 + 4 =

18. anonymous

oh i was thinking adding. silly me lol. so 6

19. UnkleRhaukus

notice that we can see in the plot, that the blue line is oscillating between 2 and 6, which agrees

20. UnkleRhaukus

so now lets look at $f(x) = −4(x − 6)^2 + 3$

21. anonymous

how would we set that up

22. UnkleRhaukus

What can you tell me about f(x)?

23. UnkleRhaukus

(what is the parent function of f )

24. anonymous

i dont get it?

25. UnkleRhaukus

its a second order polynomial, right? so its a quadratic equation, and will look like some sort of parabola

26. anonymous

is this calculus? if so, take the derivative of the function, and set to 0 to find where it has a max (or min). However, you do not need calculus. The first function, f(x)=-4(x-6)^2 + 3 is a parabola ( in the shape of a "frown" ) with a max value at its vertex. because they gave you the equation in "vertex form" y = a(x-h)^2 + k , you can read off the vertex to be (h,k) In this case, the vertex is at (6,3) for the second function, g(x)=2cos(2x-pi)+4 you should know that the max value of the cosine is 1, so the max will be g(x)= 2*1 + 4 = 6

27. UnkleRhaukus

@TavTav are you still here?

28. anonymous

yes sorry

29. anonymous

so i got g(x) but how would you get f(x)

30. UnkleRhaukus

given that f(x) is some sort of parabola, do you expect f to have both max and min values?

31. anonymous

no

32. UnkleRhaukus

$f(x)=-4(x-6)^2 + 3$ which is a bit like: $$-x^2$$ which do you expect: a max, or a min value?

33. anonymous

max

34. UnkleRhaukus

good, and the max will be when the terms under the square, will be what value?

35. anonymous

the max value would be the 3?

36. UnkleRhaukus

yeah, the max is when the terms under the square is zero, $f_\text{max}=-4(0)^2 + 3\\ \qquad=-0+3\\ \qquad=3$

37. anonymous

thank you. i need to have it in complete sentences so can you help me form those?

38. anonymous

for both g(x) and f(x)

39. UnkleRhaukus

show me what you got

40. anonymous

uum ok

41. anonymous

lol

42. UnkleRhaukus

The general idea was that we considered the parent functions $$G(X) = \cos (X)$$, and $$F(X)=-X^2$$, respectively

43. anonymous

I know how we got g(x) i just dont know how to put it in words for f(x) we used the zeros of the equation to find the maximun value?

44. UnkleRhaukus

we didn't really use the "zeroes of the equations", they are different things

45. anonymous

ohh , uhh. so how would you word it

46. anonymous

that we compared the functions to their parent functions to get the maximum value

47. UnkleRhaukus

yeah, something like that, we know how to find the max/min of the parent functions, and then we apply these results to our particular functions

48. UnkleRhaukus

scaling and shifting as specified

49. anonymous

so i can use that as the answer?

50. UnkleRhaukus

kind of. you might like to write separate paragraphs for each function

51. anonymous

okok , thank you so much!! you made this easy to understand.your a lifesaver lol