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

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UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2The function is \[g(x) = 2\cos(2x\pi)+4\] This will have maximum values when the cosine term is at maximums

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0f(x) = −4(x − 6)^2 + 3

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2do you know what the largest value of \(\cos\theta\), can ever be? (for all possible angles \(\theta\) )

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2remember 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)

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2dw:1440303568385:dw

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2The cosine function (like the sine function ) oscillates between its maximum and minimum values ; ±1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So the maximun for g(x) would be 1?

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2not quite, that max for cos theta, and hence the max for cos(2xπ) is 1

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2so the max for g(x) = 2cos(2xπ) + 4 is gmax = 2(+1) + 4 =

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2(whereas the minimum is gmin = 2(1) + 4 = 2+4 = 2 )

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2wait gmax = 2(+1) + 4 = 2 times 1 + 4 =

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh i was thinking adding. silly me lol. so 6

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2notice that we can see in the plot, that the blue line is oscillating between 2 and 6, which agrees

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2so now lets look at \[f(x) = −4(x − 6)^2 + 3 \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how would we set that up

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2What can you tell me about f(x)?

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2(what is the parent function of f )

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2its a second order polynomial, right? so its a quadratic equation, and will look like some sort of parabola

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is 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(x6)^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(xh)^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(2xpi)+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
 one year ago
Best ResponseYou've already chosen the best response.2@TavTav are you still here?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so i got g(x) but how would you get f(x)

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2given that f(x) is some sort of parabola, do you expect f to have both max and min values?

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2\[f(x)=4(x6)^2 + 3\] which is a bit like: \(x^2\) which do you expect: a max, or a min value?

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2good, and the max will be when the terms under the square, will be what value?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the max value would be the 3?

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2yeah, the max is when the terms under the square is zero, \[f_\text{max}=4(0)^2 + 3\\ \qquad=0+3\\ \qquad=3\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank you. i need to have it in complete sentences so can you help me form those?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0for both g(x) and f(x)

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2show me what you got

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2The general idea was that we considered the parent functions \(G(X) = \cos (X)\), and \(F(X)=X^2\), respectively

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I 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
 one year ago
Best ResponseYou've already chosen the best response.2we didn't really use the "zeroes of the equations", they are different things

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh , uhh. so how would you word it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that we compared the functions to their parent functions to get the maximum value

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2yeah, 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
 one year ago
Best ResponseYou've already chosen the best response.2scaling and shifting as specified

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so i can use that as the answer?

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2kind of. you might like to write separate paragraphs for each function

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okok , thank you so much!! you made this easy to understand.your a lifesaver lol
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