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Fill in the blanks  1) If f'(x)>0 on the interval [a,b], then f is______________...

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adelajda | Student, College Freshman | eNoter

Posted May 28, 2010 at 11:44 PM via web

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Fill in the blanks

 

1) If f'(x)>0 on the interval [a,b], then f is______________

2) If f is a differentiable function on the interval [a,b] and c belongs to [a,b], then f(b)-__=________

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giorgiana1976 | College Teacher | Valedictorian

Posted May 28, 2010 at 11:46 PM (Answer #1)

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 1) If f'(x)>0 on the interval [a,b], then f is increasing on that interval [a,b].

2) If f is a differentiable function on the interval [a,b] and c belongs to [a,b], then

f(b)-f(a)=f'(c)(b-a)

We've used the Mean Value Theorem and you could also write:

f'(c)=[f(b)-f(a)]/(b-a)

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neela | High School Teacher | Valedictorian

Posted May 28, 2010 at 11:49 PM (Answer #3)

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a) If f'(x) > 0, then in the interval {a,b} f(x) is increasing.

b) If f is a differentiable function in [a,b} and c belongs [a, b],

then f(b)-f(a) = (b-a) f'(c)

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giorgiana1976 | College Teacher | Valedictorian

Posted May 28, 2010 at 11:50 PM (Answer #4)

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It is all you need, to fill in the blanks properly.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted May 28, 2010 at 11:58 PM (Answer #5)

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1) If f'(x)>0 on the interval [a,b], then f is increasing on [a,b].

2) If f is a differentiable function on the interval [a,b] and c belongs to [a,b], then f(b)-f(a)=f'(c) (b-a)

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