Question

Functions f(x) and g(x) are shown below:
Using complete sentences, explain how to find the maximum value for each function and determine which function has the largest maximum y-value.

Answer 1

waiting on the graphs

Answer 2

What's the graph of f(x)?

Answer 3

f(x) = −4(x − 6)2 + 3

Answer 4

Have you learned about the First Derivative Test?

Answer 5

Normally when you say
\(\color{#000000 }{ \displaystyle y=\cos(x) }\)

Then, \(\color{#000000 }{ \displaystyle-1<y<1 }\), right?
(Because \(\color{#000000 }{ \displaystyle -1<\cos(x)<1 }\))

Answer 6

And in fact, even if you say that
\(\color{#000000 }{ \displaystyle y=\cos[a(x)] }\)

Then, the cosine is also going to be between -1 and 1

Answer 7

So, the maximum of
\(\color{#000000 }{ \displaystyle y=\cos[a(x)] }\)
or, \(\color{#000000 }{ \displaystyle y=\cos[x] }\)

would be?

Answer 8

Based on your answer to this question, you have to multiply that maximum times 2 (since your cosine function is multiplied times a scale factor of 2), and shift your maximum by 4 units up (since the cosine function you are dealing with is shifted 4 units up).

Answer 9

For \(\color{#000000 }{ \displaystyle -4(x - 6)^2 + 3 }\),
it is an opening down parabola, and it's maximum is the vertex
(which can be foun by completing the square, or graphing).

Answer 10

thank you!