Solution Found!
Answer: Designing a function S ketch the graph of a
Chapter 7, Problem 22E(choose chapter or problem)
19-22. Designing a function Sketch the graph of a continuous function f on [0, 4] satisfying the given properties.
f'(x) = 0 at x = 1 and 3: f'(2) is undefined; f has an absolute maximum at x = 2; f has neither a local maximum nor a local minimum at x = 1; and f has an absolute minimum at x = 3.
Questions & Answers
QUESTION:
19-22. Designing a function Sketch the graph of a continuous function f on [0, 4] satisfying the given properties.
f'(x) = 0 at x = 1 and 3: f'(2) is undefined; f has an absolute maximum at x = 2; f has neither a local maximum nor a local minimum at x = 1; and f has an absolute minimum at x = 3.
ANSWER:STEP_BY_STEP SOLUTION Step_1 When an output value of a function is a maximum or a minimum over the entire domain of the function, the value is called the absolute maximum or the absolute minimum. Let f be a function with domainD and let c be a fixed constant in D. Then the output value f ) is the 1. Absolute maximum value of f on D if and only if f(x) f(c) , for all x in D. 2. Absolute minimum value of f on D if and only if f(c) f(x) , for all x in D. Step-2 Let f be defined on the interval [a,b] , and x be the 0nterior point on [a,b]. A function f has a local maximum or relative maximum at a point x if the values 0 f(x) of f for x ‘near’ x are0all less than f(x ). 0 That is , f(x) f(x ) 0 Thus, the graph of f near x h0s a p eak at x .