Answer the Problem $f ( x ) = a x ^ { 4 } + b x ^ { 3 } + c x ^ { 2 } + d x + e , a \neq 0$

question 118

Essay

Answer the problem.
-Consider the quartic function $f ( x ) = a x ^ { 4 } + b x ^ { 3 } + c x ^ { 2 } + d x + e , a \neq 0$ . Must this function have at least one critical point? Give reasons for your answer. (Hint: Must $f ^ { \prime } ( x ) = 0$ for some $x$ ?) How many local extreme values can $f$ have?

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