Find the absolute maximum and absolute minimum values of the

luipieduq3 2021-12-04 Answered
Find the absolute maximum and absolute minimum values of the function : f(x)=x48x210 on interval = [-4,1]
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Prioned
Answered 2021-12-05 Author has 11 answers
Find the absolute maximum and absolute minimum values of the function f(x)=x48x210 on the interval [-4,1] as follows.
On the interval [-4,1], the critical points of the function f(x)=x48x210 are x=-2 and x=0.
Now evaluate the function at the critical points x=-2 and x=0 and at the endpoints x=-4 and x=1 as shown below.
f(4)=(4)48(4)210=25612810=118
f(2)=(2)48(2)210=163210=26
f(0)=(0)48(0)210=0010=10
f(1)=(1)48(1)210=1810=17
Comparing the above values, it is clear that the absolute maximum and minimum of f on the interval [-4,1] are,
Absolute maximum : (x,f(x))=(-4, 118)
Absolute minimum : (x,f(x))=(-2, -26)
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