What are the absolute extrema of $f (x) = 8 x^{3} - 24 x + 3 \in [- \infty, \infty]$ $f(x)=8x^3 - 24x + 3 in[-oo,oo]$ ?

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Answer 1 · 2015-11-10T09:33:19

$\pm \infty$ $+-oo$

Since this is a cubic polynomial function, it is unbounded and so its absolute extrema are $\pm \infty$ $+-oo$ .

This is clear from its graph given below

graph{8x^3-24x+3 [-46.22, 46.25, -23.12, 23.14]}

What are the absolute extrema of f(x)=8x^3 - 24x + 3 in[-oo,oo]f(x)=8x3−24x+3∈[−∞,∞]f(x)=8x^3 - 24x + 3 in[-oo,oo]?