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

f (x) g (x)

f (x) = 3x2 + 12x + 16 graph of sine function which starts at 0 comma 0 and decreases to the minimum pi over 2, then increases to the maximum of 3 pi over 2 then decreases to 2 pi where the cycle repeats

Courtesy of Texas Instruments

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

Question

Mathematics

Watkins

24 March, 08:59

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

f (x) g (x)

f (x) = 3x2 + 12x + 16 graph of sine function which starts at 0 comma 0 and decreases to the minimum pi over 2, then increases to the maximum of 3 pi over 2 then decreases to 2 pi where the cycle repeats

Courtesy of Texas Instruments

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

+2

Answers (1)

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Kason Estes · Answer 1

f' (x) = 6 x + 12

6 x + 12 = 0 6 x = - 12 x = - 2 f ( - 2) 0 12 - 24 + 16 = 4 f (x) min = 4 g' (x) = 4 cos (2 x - π) 4 cos (2 x - π) = 0 cos (2 x - π) = 0 2 x - π = 3π / 2 2 x = 5π / 2 x = 5π/4 g (5π/4) = 2 sin (5π/2 - π) + 4 = 2 (sin 3π/2) + 4 = - 2 + 4 = 2 g (x) min = 2