## anonymous one year ago f(x) g(x)

1. marinos

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

2. anonymous

yes @marinos

3. anonymous

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

4. anonymous

5. marinos

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

6. anonymous

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

7. anonymous

8. anonymous

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

9. anonymous

B

10. anonymous

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

11. marinos

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 ?

12. anonymous

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)

13. anonymous

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

14. anonymous

Is what I'm saying make sense jacy?

15. marinos

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

16. anonymous

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

17. marinos

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.

18. marinos

@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)

19. anonymous

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

20. marinos

You are welcome.