Suppose fe Cla,b] and f'(x) exists on (a,b). Show that if f'(x)0 for all x in (a, b), then there can exist at most one number p in [a, b] with f(p) = 0.
Suppose fe Cla,b] and f'(x) exists on (a,b). Show that if f'(x)0 for all x in (a, b), then there can exist at most one number p in [a, b] with f(p) = 0.
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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![Suppose fe Cla,b] and f'(x) exists on (a, b). Show that if f'(x) #0 for all x in (a, b), then there
can exist at most one number p in [a, b] with f(p) = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34700fa5-efb1-4bfb-9b6d-159218f0b591%2Fe23b1f31-f159-4fc6-a8bb-848fdbc5ceae%2Fs3u0q8n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose fe Cla,b] and f'(x) exists on (a, b). Show that if f'(x) #0 for all x in (a, b), then there
can exist at most one number p in [a, b] with f(p) = 0.
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