Find the critical points and the interval on which the given function is increasing or decreasing, and apply the First Derivative Test to each critical point. Let ƒ(x) = ²x¹ + 3⁄4 x³ + −2² r² − 96x 3 There are three critical points. If we call them C₁, C2, and c3, with c₁ < C₂ < c3, then C1 = C₂ = and c3 = Is f a maximum or minumum at the critical points? At C₁, fis ? û At C2, f is ? î At C3, f is? î These three critical give us four intervals. The left-most interval is and on this interval f is ? The next interval (going left to right) is Next is the interval Finally, the right-most interval is On this interval f is ? ¹0. On this interval f is ? On this interval f is ? while f¹ is ? while f' is ? î while f' is? î while f' is?

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