Consider the equation below. f(x) = x4 − 8x2 + 8 (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 − 8x2 + 8 (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 − 8x2 + 8 (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) attains a local maximum 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 case, f(a) attains a local maximum value f(x) at x=a .
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