The (-2, 80) is a relative minimum, (4, -136) relative maximum option (C) is correct.
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The cubic function:
f(x) = 2x³ - 6x² - 48x + 24
Find f'(x):
f'(x) = 6x² - 12x - 48
Equate f'(x) to zero:
6x² - 12x - 48 = 0
Find the roots of the quadratic equation:
x = -2
x = 4
Find f''(x):
f''(x) = 12x - 12
Plug x = -2
f''(-2) = -24 - 12 = -36 < 0
At x = -2 f(x) is minimum
f(-2) = 80
Plug x = 4
f''(4) = 48 - 12 = 36 > 0
At x = 4 f(x) is maximum
f(4) = -136
Thus, the (-2, 80) is a relative minimum, and (4, -136) relative maximum option (C) is correct.
Learn more about the function here:
brainly.com/question/5245372
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