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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
Worksheet 3.1—Extrema on an Interval Show all work. No...
- WS 03.1 Extrema on an Interval
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 ...
To locate the absolute extrema of a continuous function on a closed interval, you need only compare the y-values of all critical points. 11. If and decreases through x c, then x c locates a local minimum value for the function. 12. Absolute extrema of a continuous function on a closed interval can occur only at endpoints or critical points.
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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 ...
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, ∞ ) .
Understand the definition of relative extrema of a function on an open interval. Find extrema on a closed interval. In calculus, much effort is devoted to determining the behavior of a function f on an interval I. Does f have a maximum value on I? Does it have a minimum value? Where is the function increasing? Where is it decreasing?
