Find the absolute minimum and absolute maximum values of f on the given interval. f(t) = t 25 − t2 , [−1, 5]

Absolute minimum: f(-1) = -2

              Absolute maximum: f() = 12.5

Step-by-step explanation: To determine minimum and maximum values in a function, take the first derivative of it and then calculate the points this new function equals 0:

f(t) =

f'(t) =

f'(t) =

f'(t) = = 0

For this function to be zero, only denominator must be zero:

t = ±

≠ 0

t = ± 5

Now, evaluate critical points in the given interval.

t = and t = - 5 don't exist in the given interval, so their f(x) don't count.

f(t) =

f(-1) =

f(-1) =

f(-1) =

f() =

f() = 12.5

f(5) =

f(5) = 0

Therefore, absolute maximum is f() = 12.5 and absolute minimum is

f(-1) = .

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