Find the absolute maximum and minimum value of the given

kolonelyf4

kolonelyf4

Answered question

2021-12-05

Find the absolute maximum and minimum value of the given function on the specified interval.
f(x)=2x3+3x212x7 on [3,0]

Answer & Explanation

pseudoenergy34

pseudoenergy34

Beginner2021-12-06Added 22 answers

Step 1
Given function is f(x)=2x3+3x212x7 on [3,0]
find the absolute maximum and minimum value of the function
Step 2
let f(x)=2x3+3x212x7
differentiate it wrt x
f(x)=6x2+6x12
let f'(x)=0
6x2+6x12=0
6(x2+x2)=0
x2+2xx2=0
x(x+2)-1(x+2)=0
(x+2)(x-1)=0
x=-2 or 1
Since the specified interval is [-3,0]
let’s ignore x=1 and consider x=-2
Let’s find the value of f(x) at x=-2 and [-3,0]
f(2)=2(2)3+3(2)212(2)7
f(-2)=-16+12+24-7
f(-2)=13
f(3)=2(3)3+3(3)212(3)7
f(-3)=-54+27+36-7
f(-3)=2
f(0)=0+0-0-7
f(0)=-7
Thus the absolute maximum value is 13 at x=-2
and absolute minimum value is -7 at x=0

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