Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval - ∞ , x 1 and decreases on the interval x 1 , ∞ , then f x 1 is a local minimum value.
Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval - ∞ , x 1 and decreases on the interval x 1 , ∞ , then f x 1 is a local minimum value.
Solution Summary: The author explains that if the function f increases on the interval (-infty,x_1) and decreases, then it is a local
Determine if the statemment is true or false. If the statement is false, then correct it and make it true.
If the function
f
increases on the interval
-
∞
,
x
1
and decreases on the interval
x
1
,
∞
, then
f
x
1
is a local minimum value.
Formula Formula A function f ( x ) is also said to have attained a local minimum at x = a , if there exists a neighborhood ( a − δ , a + δ ) of a such that, f ( x ) > f ( a ) , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a f ( x ) − f ( a ) > 0 , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a In such a case f ( a ) is called the local minimum value of f ( x ) at x = a .
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