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MaxWong

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MaxWong  13 janv. 2019
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a)

f(x) is {positivenegative} when f(x) is {strictly increasingstrictly decreasing}.

f(x) is strictly increasing on the interval (,1)(3,) and strictly decreasing on the interval (1,3).

 

What about when x = 1 or x = 3?

 

Let ε be an arbitrary constant, infinitesmally small.

f(1ε)>0 and f(1+ε)<0

At x = 1, local maximum of f(x) occurs.

 

f(3ε)<0 and f(3+ε)>0

At x = 3, local minimum of f(x) occurs.

 

f(x) is {increasingdecreasingconstant} when f(x) {is convexis concavehas a point of inflexion}.

f(x) is concave on the interval (,2) and is convex on the interval (2,).

Point of inflexion of f(x) occurs at x=2.

 

b)

f(x) is {increasingdecreasingconstant} when f(x) is {positivenegative0}.

f(x) is negative on the interval (,2) and is positive on the interval (2,).

f(2)=0

.
14 avr. 2020