anonymous
  • anonymous
explain how to find the maximum value for each function and determine which function has the largest maximum y-value.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
anonymous
  • anonymous
@UnkleRhaukus
UnkleRhaukus
  • UnkleRhaukus
The function is \[g(x) = 2\cos(2x-\pi)+4\] This will have maximum values when the cosine term is at maximums

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anonymous
  • anonymous
f(x) = −4(x − 6)^2 + 3
UnkleRhaukus
  • UnkleRhaukus
do you know what the largest value of \(\cos\theta\), can ever be? (for all possible angles \(\theta\) )
anonymous
  • anonymous
no
UnkleRhaukus
  • 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)
anonymous
  • anonymous
ok ok , i get that
UnkleRhaukus
  • UnkleRhaukus
|dw:1440303568385:dw|
UnkleRhaukus
  • UnkleRhaukus
The cosine function (like the sine function ) oscillates between its maximum and minimum values ; ±1
anonymous
  • anonymous
okk
anonymous
  • anonymous
So the maximun for g(x) would be 1?
UnkleRhaukus
  • UnkleRhaukus
not quite, that max for cos theta, and hence the max for cos(2x-π) is 1
UnkleRhaukus
  • UnkleRhaukus
so the max for g(x) = 2cos(2x-π) + 4 is gmax = 2(+1) + 4 =
anonymous
  • anonymous
so 7 lol
UnkleRhaukus
  • UnkleRhaukus
(whereas the minimum is gmin = 2(-1) + 4 = -2+4 = 2 )
UnkleRhaukus
  • UnkleRhaukus
wait gmax = 2(+1) + 4 = 2 times 1 + 4 =
anonymous
  • anonymous
oh i was thinking adding. silly me lol. so 6
UnkleRhaukus
  • UnkleRhaukus
notice that we can see in the plot, that the blue line is oscillating between 2 and 6, which agrees
UnkleRhaukus
  • UnkleRhaukus
so now lets look at \[f(x) = −4(x − 6)^2 + 3 \]
anonymous
  • anonymous
how would we set that up
UnkleRhaukus
  • UnkleRhaukus
What can you tell me about f(x)?
UnkleRhaukus
  • UnkleRhaukus
(what is the parent function of f )
anonymous
  • anonymous
i dont get it?
UnkleRhaukus
  • UnkleRhaukus
its a second order polynomial, right? so its a quadratic equation, and will look like some sort of parabola
anonymous
  • 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
UnkleRhaukus
  • UnkleRhaukus
@TavTav are you still here?
anonymous
  • anonymous
yes sorry
anonymous
  • anonymous
so i got g(x) but how would you get f(x)
UnkleRhaukus
  • UnkleRhaukus
given that f(x) is some sort of parabola, do you expect f to have both max and min values?
anonymous
  • anonymous
no
UnkleRhaukus
  • 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?
anonymous
  • anonymous
max
UnkleRhaukus
  • UnkleRhaukus
good, and the max will be when the terms under the square, will be what value?
anonymous
  • anonymous
the max value would be the 3?
UnkleRhaukus
  • UnkleRhaukus
yeah, the max is when the terms under the square is zero, \[f_\text{max}=-4(0)^2 + 3\\ \qquad=-0+3\\ \qquad=3\]
anonymous
  • anonymous
thank you. i need to have it in complete sentences so can you help me form those?
anonymous
  • anonymous
for both g(x) and f(x)
UnkleRhaukus
  • UnkleRhaukus
show me what you got
anonymous
  • anonymous
uum ok
anonymous
  • anonymous
lol
UnkleRhaukus
  • UnkleRhaukus
The general idea was that we considered the parent functions \(G(X) = \cos (X)\), and \(F(X)=-X^2\), respectively
anonymous
  • 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?
UnkleRhaukus
  • UnkleRhaukus
we didn't really use the "zeroes of the equations", they are different things
anonymous
  • anonymous
ohh , uhh. so how would you word it
anonymous
  • anonymous
that we compared the functions to their parent functions to get the maximum value
UnkleRhaukus
  • 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
UnkleRhaukus
  • UnkleRhaukus
scaling and shifting as specified
anonymous
  • anonymous
so i can use that as the answer?
UnkleRhaukus
  • UnkleRhaukus
kind of. you might like to write separate paragraphs for each function
anonymous
  • anonymous
okok , thank you so much!! you made this easy to understand.your a lifesaver lol

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