Find the absolute maximum and minimum values of the following

Pearl Carney

Pearl Carney

Answered question

2021-12-04

Find the absolute maximum and minimum values of the following function over the indicated interval, and indicate the x-values at which they occur.
f(x)=13x3+52x26x+8;[9,3]
The absolute maximum value is B at x= B
The absolute minimum value is B at x= B

Answer & Explanation

Vincent Diaz

Vincent Diaz

Beginner2021-12-05Added 19 answers

Step 1
Solution:
Given f(x)=13x3+52x26x+8 [9,3]
To find Absolute maximum and minimum
Formula:
ddx(xn)=nxn1
Step 2
f(x)=13x3+52x26x+8 [9,3]
Now differentiating with respect to x on both side
f(x)=x2+5x6
x2+5x6=0
x=1, x=-6
when x=1 f(1)=13+526+8=4.83
x=-6 f(-6)=62
x=-9 f(-9)=21.2
x=3 f(3)=21.5
at x=1 the f(x) is absolute minimum
and the minimum value is 4.83
at x=-6 the f(x) is absolute maximum
and the maximum value is 62

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