Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = \ln(x^{2} + 5x + 13), \left[−3, 1\right]

Wotzdorfg 2020-10-25 Answered
Find the absolute maximum and absolute minimum values of f on the given interval.
f(x)=ln(x2+5x+13),[3,1]
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Expert Answer

Aamina Herring
Answered 2020-10-26 Author has 85 answers

Step 1
The given function
f(x)=ln(x2+5x+13),[3,1]
Differentiate with respect to x
fprime(x)=d(ln(x2+5x+13))d(x2+5x+13)×d(x2+5x+13)dx
=2x+5(x2+5x+13)
Step 2
fprime(x)=0
x=52
So critical points
x=52,3,1
f(2.5)=ln((2.5)25×2.5+13)=1.9
f(3)=ln((3)25×3+13)=1.95
f(1)=ln((1)2+5×1+13)=ln(19)=2.94
Step 3
Absolute maximum value = 2.94
Absolute minimum value = 1.9

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Jeffrey Jordon
Answered 2021-11-14 Author has 2087 answers

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