Find the absolute maximum and absolute minimum values of the function: f(x)=5x^{7}−7x^{5}−7 on the interval \left[−3,4\right]

ankarskogC 2021-02-09 Answered
Find the absolute maximum and absolute minimum values of the function:
f(x)=5x77x57 on the interval [3,4]
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Expert Answer

Velsenw
Answered 2021-02-10 Author has 91 answers

Step 1
We find the critical points by solving f(x)=0
Use power rule to find f(x)
f(x)=5x77x57
f(x)=35x635x4
35x635x4=0
35x4(x21)=0
35x4(x+1)(x1)=0
x=0,1,1
Step 2
Then we find the f(x) values at the endpoints and at the critical points
f(3)=5(3)77(3)57=9241 (min)
f(4)=5(4)77(4)57=74745 (max)
f(0)=5(0)77(0)57=7
f(1)=5(1)77(1)57=5
f(1)=5(1)77(1)57=9
Result: Absolute maximum value= 74745 at x=4
Absolute minimum value= -9241 at x=3

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Jeffrey Jordon
Answered 2021-11-14 Author has 2070 answers

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