Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x/x^2+9 (a) Find the interval on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.) (b) Find the local maximum and minimum values of f. local minimum value local maximum value (c) Find the inflection points. (Order your answers from smallest to largest x, then from smallest to largest y.) (x, y) = (x, y) = (x, y) = Find the interval on which f is concave up. (Enter your answer using interval notation.) Find the interval on which f is concave down.(Enter your answer using interval notation.)
Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x/x^2+9 (a) Find the interval on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.) (b) Find the local maximum and minimum values of f. local minimum value local maximum value (c) Find the inflection points. (Order your answers from smallest to largest x, then from smallest to largest y.) (x, y) = (x, y) = (x, y) = Find the interval on which f is concave up. (Enter your answer using interval notation.) Find the interval on which f is concave down.(Enter your answer using interval notation.)
Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x/x^2+9 (a) Find the interval on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.) (b) Find the local maximum and minimum values of f. local minimum value local maximum value (c) Find the inflection points. (Order your answers from smallest to largest x, then from smallest to largest y.) (x, y) = (x, y) = (x, y) = Find the interval on which f is concave up. (Enter your answer using interval notation.) Find the interval on which f is concave down.(Enter your answer using interval notation.)
Consider the equation below. (If an answer does not exist, enter DNE.)
f(x) = x/x^2+9
(a)
Find the interval on which f is increasing. (Enter your answer using interval notation.)
Find the interval on which f is decreasing. (Enter your answer using interval notation.)
(b)
Find the local maximum and minimum values of f.
local minimum value
local maximum value
(c)
Find the inflection points. (Order your answers from smallest to largest x, then from smallest to largest y.)
(x, y)
=
(x, y)
=
(x, y)
=
Find the interval on which f is concave up. (Enter your answer using interval notation.)
Find the interval on which f is concave down.(Enter your answer using 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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