The function f(x)=2x^{3}-33x^{2}+168x+9 has one local minimum and one local

Halkadvalseln 2021-11-23 Answered
The function f(x)=2x333x2+168x+9 has one local minimum and one local maximum.
Use a graph of the function to estimate these local extrema.
This function has a local minimum at x=?
with output value:
and a local maximum at x=?
with output value:
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Expert Answer

Muspee
Answered 2021-11-24 Author has 13 answers
Step 1
To estimate (approximate calculation) the local maximum and local minimum of the given function
y=f(x)
Step 2
Now we know the critical values are at x=4 and x=7. For further analysis graph the function between x=3 and x=8 (in the neighbourhood of the critical points)
f(x)=2x333x2+168x+9
The local max and min occur when
f(x)=6x266x+168
=6(x211x+28)
=6(x4)(x7)=0
so, x=4, x=7
Step 3
Estimates: local minimum at x=7 with value 255, local maximum at x=4 with value 280
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