Functions f (x) and g (x) are shown below:

f (x) g (x)

f (x) = - 4 (x - 6) 2 + 3 graph of cosine function which starts at 0 comma 2 and increases to the maximum at pi over 2 then decreases to the minimum at 2 pi where the cycle repeats

Courtesy of Texas Instruments

Using complete sentences, explain how to find the maximum value for each function and determine which function has the largest maximum y-value.

Question

Anya Reed

Mathematics

18 March, 13:18

Functions f (x) and g (x) are shown below:

f (x) g (x)

f (x) = - 4 (x - 6) 2 + 3 graph of cosine function which starts at 0 comma 2 and increases to the maximum at pi over 2 then decreases to the minimum at 2 pi where the cycle repeats

Courtesy of Texas Instruments

Using complete sentences, explain how to find the maximum value for each function and determine which function has the largest maximum y-value.

+1

Answers (1)

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Damon Hickman · Answer 1

F (x) = - 4 (x-6) ^2 + 3

Maximum value is found by solving the root of the first derivative. that root is where the maximum value is.

f ' (x) = - 8 (x - 6) = 0.

So x = 6 and that's the maximum value. f (6) = 3

2cos (2x - π) + 4 is a trig function. The maximum value of cosine function is 1.

So the maximum value would be 2 (1) + 4 = 6.