# Find the absolute maximum and absolute minimum values of the

Find the absolute maximum and absolute minimum values of the function : $f\left(x\right)={x}^{4}-8{x}^{2}-10$ on interval = [-4,1]
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Find the absolute maximum and absolute minimum values of the function $f\left(x\right)={x}^{4}-8{x}^{2}-10$ on the interval [-4,1] as follows.
On the interval [-4,1], the critical points of the function $f\left(x\right)={x}^{4}-8{x}^{2}-10$ 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.
$f\left(-4\right)={\left(-4\right)}^{4}-8{\left(-4\right)}^{2}-10=256-128-10=118$
$f\left(-2\right)={\left(-2\right)}^{4}-8{\left(-2\right)}^{2}-10=16-32-10=-26$
$f\left(0\right)={\left(0\right)}^{4}-8{\left(0\right)}^{2}-10=0-0-10=-10$
$f\left(1\right)={\left(-1\right)}^{4}-8{\left(-1\right)}^{2}-10=1-8-10=-17$
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)