Find the absolute maxima and minima for f(x) on the interval [a, b]. f(x) = 2x3 − 6x2 − 18x − 4, [−10, 10]

Step-by-step explanation:

Given the function

f(x) = 2x3 − 6x2 − 18x − 4 on the interval [-10, 10]

At the end point x = -10

f(-10) = 2(-10)³ − 6(-10)² − 18(-10) − 4

f(-10) = 2(-1000)-6(100)+180-4

f(-10) = -2000-600+176

f(-10) = -1824

At the end point x = 10

f(10) = 2(10)³ − 6(10)² − 18(10) − 4

f(10) = 2(1000)-6(100)-180-4

f(10) = 2000-600-184

f(10) = 1400-184

f(10) = 1216

Hence the absolute minimum is at f(x) = -1824 and maximum is at f(x) = 1216

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

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this shows a reflection over the x-axis and is translated one unit down and 6 units to the right (x + 6, y - 1)

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