Consider the equation below. f(x) = x4 − 2x2 + 4 (a) Find the interval on which f is increasing. (Enter your answer in interval notation.) Find the interval on which f is decreasing. (Enter your answer in interval notation.) (b) Find the local minimum and maximum values of f. local minimum local maximum (c) Find the inflection points. (x, y) = (smaller x-value) (x, y) = (larger x-value)Find the interval on which f is concave up. (Enter your answer in interval notation.) Find the interval on which f is concave down. (Enter your answer in interval notation.)
Consider the equation below. f(x) = x4 − 2x2 + 4 (a) Find the interval on which f is increasing. (Enter your answer in interval notation.) Find the interval on which f is decreasing. (Enter your answer in interval notation.) (b) Find the local minimum and maximum values of f. local minimum local maximum (c) Find the inflection points. (x, y) = (smaller x-value) (x, y) = (larger x-value)Find the interval on which f is concave up. (Enter your answer in interval notation.) Find the interval on which f is concave down. (Enter your answer in interval notation.)
Consider the equation below. f(x) = x4 − 2x2 + 4 (a) Find the interval on which f is increasing. (Enter your answer in interval notation.) Find the interval on which f is decreasing. (Enter your answer in interval notation.) (b) Find the local minimum and maximum values of f. local minimum local maximum (c) Find the inflection points. (x, y) = (smaller x-value) (x, y) = (larger x-value)Find the interval on which f is concave up. (Enter your answer in interval notation.) Find the interval on which f is concave down. (Enter your answer in interval notation.)
(a) Find the interval on which f is increasing. (Enter your answer in interval notation.)
Find the interval on which f is decreasing. (Enter your answer in interval notation.)
(b) Find the local minimum and maximum values of f.
local minimum
local maximum
(c) Find the inflection points.
(x, y) =
(smaller x-value)
(x, y) =
(larger x-value)
Find the interval on which f is concave up. (Enter your answer in interval notation.)
Find the interval on which f is concave down. (Enter your answer in interval notation.)
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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