Find the absolute maximum and absolute minimum values of f on the given interval

abondantQ

abondantQ

Answered question

2021-09-10

Find the absolute maximum and absolute minimum values of f on the given interval. Give exact answers using radicals, as necessary.
t-(cube root of t) in [ -1,5]

Answer & Explanation

Alannej

Alannej

Skilled2021-09-11Added 104 answers

Compute critical points as follows.
f(t)=tt13
f(t)=ddt(tt13)=113t23
the critical numbers are the value of domain in which f(x)=0 or f(x) does not exist.
f(t)=0
113t23
t23=13
t=(13)23
note that f'(t) does not exist at t=0.
Thus, the critical numbers are (13)23,0

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