Find the absolute extremum values of f(x)=x^{2}-5x+18 over the interval

Irvin Dukes

Irvin Dukes

Answered question

2021-12-14

Find the absolute extremum values of f(x)=x25x+18 over the interval [1,5].

Answer & Explanation

Kayla Kline

Kayla Kline

Beginner2021-12-15Added 37 answers

Step 1
The given function is f(x)=x25x+18 in the interval [1,5]
Find the critical point:
f(x)=ddx(x25+18)
=2x-5
2x-5=0 [set f'(x)=0]
2x=5
x=52
Thus, the critical points of the function that lie in the given interval [1,5].
Now evaluate the function at the critical points and the end points of the interval
f(1)=(1)25(1)+18
=1-5+18
=14
f(52)=(52)25(52)+18
=254252+18
=2550+724
=474
Step 3
f(5)=(5)25(5)+18
=25-25+18
=18
Thus, the absolute extremum value is 18 occurs and it at 5.

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