Question

f(x) g(x)

Answer 1

Do you mean the following functions ?
\[f(x)=-4\left( x-6 \right)^{2}+3\]
and
\[g(x)=2\cos \left( 2x-\pi \right)+4\]

Answer 2

yes @marinos

Answer 3

The maximum of cosine is 1, then g max is 2+4=2
The the vertex of the flipped parabola is when is 0, cause it's negative otherwise. So f max is 0+3 =3

Answer 4

can you explain how @Ahmad-nedal

Answer 5

Remember that a square is always non-negative and that the absolute value of (sine and) cosine function(s) is at most 1.

Answer 6

But the thing is, these two values are not satisfied at the same x coordinate, I think you will now be needing calculus 1 to find that point where x gets you the maximum

Answer 7

What is your grade right now @jacey.stewart ?

Answer 8

You use equation x=-b/2a to find the maximum Im just confused on the cosine part

Answer 9

B

Answer 10

The maximum of any sinsouidal function (since, cosx) is 1, therefore the maximum of cosine is 2

Answer 11

We have that \[\left( x-6 \right)^{2}\ge0\] since it is a square. Therefore \[-4\left( x-6 \right)^{2}\le0\] so \[f(x)=-4\left( x-6 \right)^{2}+3\le3\] implying that the maximum value of the function \[f(x)\] is 3.

Can you argue similarly for the other function ?

Answer 12

In my opinion, I think the question is not well written. Again if the maximum of f and g are achieved in two different x coordinates. Thus you cannot determine which point gives you the maximum MULTIPLE OF F(X) AND G(X)

Answer 13

I repeat, you may need deffrentiation to find the maximum of f times g

Answer 14

Is what I'm saying make sense jacy?

Answer 15

@Ahmad-nedal No differentiation is needed for these functions. There maximum value can be obtained using inqualities.

Answer 16

I think it ultimately asked for the maximum of the multiple of F and G, isn't she?

Answer 17

Since \[\cos \left( 2x-\pi \right)\le1\] we have \[2\cos \left( 2x-\pi \right)\le2\] so \[g(x)=2\cos \left( 2x-\pi \right)+4\le2+4=6\] therefore the maximum value of this function is 6, and it is the greatest of the maximum values of the two initial functions.

Answer 18

@Ahmad-nedal I didn't see any reference to the product of f(x) and g(x) (in which case you do need differentiation to find the max value)

Answer 19

Then you are right, it will be kinda trevial if considered two separate questions
Thanksfor clarification

Answer 20

You are welcome.