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Curve Sketching
5. Graphical Applications of Derivatives / Curve Sketching / Problem 2
Problem 2

Graph the function f(x)=6−6x23+x83f\(\left\)(x\(\right\))=6-6x^{\(\frac\)23}+x^{\(\frac\)83}. The first and second derivative are given.
f′(x)=−4x13+83x53f^{\(\prime\)}\(\left\)(x\(\right\))=-\(\frac{4}{x^{\frac13}\)}+\(\frac\)83x^{\(\frac\)53}
f′′(x)=43x43+409x23f^{\(\prime\]\prime\)}\(\left\)(x\(\right\))=\(\frac{4}{3x^{\frac43}\)}+\(\frac{40}{9}\)x^{\(\frac\)23}