Question

Determine the location and values of absolute maximum and absolute minimum for given function: (-x+3)^4 where 0≤x≤3

Answer 1

Answer:

so the absolve to maximum is 16

Answer 2

Answer:

The absolute maximum value of f(x) is 0 and the absolute minimum value of f(x) is -108.

Step-by-step explanation:

Given, function $f(x) = (-x+3)^{4}$   where,  0≤x≤3

Now, to find the absolute maximum and absolute minimum values we need to first differentiate the function f(x) and equate it to 0.

∴ $f'(x) = -4(-x+3)^{3}$ $= 0$

⇒ $x = 3$

Then, we evaluate the value of f(x) at critical point x=3 and at the end points of the interval [0,3].

f(3) = 0

f(0) = -4 × 3 × 3 × 3 = -108

Hence, absolute maximum value of f(x) on [0,3] is 0 occurring at x = 3 and absolute minimum value of f(x) on [0,3] is -108 occurring at x = 0.

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