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Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = [tex]\frac{1}{8}(3x-1) , x\leq 3[/tex]

Respuesta :

Answer:

local minimum: DNE

absolute minimum: DNE

local maximum: DNE

absolute maximum: (3, 1)

Step-by-step explanation:

The equation:

f(x) = 1/8*(3x - 1)

is an equation of a line. Applying distributive property:

f(x) = 1/8*3x - 1/8

f(x) = 3/8x - 1/8

Given that f(x) is a line with a positive slope (3/8) it doesn't have a minimum. It has an absolute maximum because the domain is restringed to x values less than or equal to 3. Replacing with x = 3 into f(x):

f(3) = 3/8(3) - 1/8 = 1

then, the maximum is located at (3, 1)

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