# 4.3 - 4.3 Connecting f and f with the Graph of f First...

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Calculus Section 4.3 Page9 4.3 Connecting f and f with the Graph of f First Derivative Test for Local Extrema Theorem 4 First Derivative Test for Local Extrema The following test applies to a continuous function f x ( ) . At a critical point c : 1. If f changes sign from positive to negative at c 2. If f changes sign from negative to positive at c 3. If f does not changes sign from positive to negative at c At a left endpoint a : If f < 0 f > 0 ( ) for x > a At a right endpoint a : If f < 0 f > 0 ( ) for x > a Example 1 Using the First Derivative Text a) Find the critical points of f x ( ) = x 3 - 12 x - 5. Find the function’s local and absolute extreme values. Identify the intervals on which f is increasing and decreasing. Solve Analytically Verify Graphically

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Calculus Section 4.3 Page 10 b) Find the critical points of f x ( ) = x 2 - 3 ( ) e x . Find the function’s local and absolute extreme values. Identify the intervals on which
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4.3 - 4.3 Connecting f and f with the Graph of f First...

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