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Worksheet 3.1—Extrema on an Interval Show all work. No calculator, except on problem #5d & 6. Short Answer 1. Let f be the functioned defined on [−1,2] by fx x x( )=322/3 −. (a) Find the domain of fx( ). (b) Find fx′( ) and the domain of fx′( ). (c) Determine if the EVT applies to fx( ) on the given interval. If it does, find the max ...
- WS 03.1 Extrema on an Interval
6. (Calculator Permitted) Using your calculator’s equation...
- WS 03.1 Extrema on an Interval
6. (Calculator Permitted) Using your calculator’s equation solving capability (not just its max/min finding ablity), find the extrema of the ( ) ln xex fx x − = on the interval [1,3]. Be sure to show the equation you’re solving and you justification via the Closed Interval Argument.
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Decide whether Rolle’s Theorem can be applied to f(x) = x3 – 2x2 on the interval [0, 2]. If Rolle’s Theorem can be applied, find all values of c in the interval such that f’(c) = 0. If Rolle’s Theorem cannot be applied, state why. increasing (‐ ∞ , 0 ); decreasing ( 0, ∞ ) .
For the following, find all relative extrema, points of inflection, and intervals of concavity. Then use a graphing calculator to graph the function and confirm you answers.
Extrema a. For "1 $ x $ 4, %nd all values of x at which f has a relative extreme. For each of these x-values, determine whether f has a relative maximum or minimum. Justify your answer. b. For "1 ≤ x ≤ 4, %nd the maximum value of f. Justify your answer. c. On the axes provided, sketch the graph of a function that has all the characteristics ...
Definition of Absolute Extrema Let f be defined on an interval I containing c. 1. f (c) is the minimum of f on the interval I if f (cfx)≤ ( ) for all x in I. 2. f (c) is the maximum of f on the interval I if f (cfx)≥ ( ) for all x in I. The Extreme Value Theorem If f is continuous on a closed interval [a, b], then f has both a minimum and a ...
