11. given f(x)=x3-4x2+5x-2 a.) State the y-intercept b.) Use the first derivative test, find all critical values, state the intervals where f(x) is increasing and any local maximum or minimum values for x. Show all work. c.) Use the second derivative test, find all critical values, find the intervals where f(x) is concave up or concave down, and state the x-coordinate for the inflection point if it exists. Show all work
11. given f(x)=x3-4x2+5x-2 a.) State the y-intercept b.) Use the first derivative test, find all critical values, state the intervals where f(x) is increasing and any local maximum or minimum values for x. Show all work. c.) Use the second derivative test, find all critical values, find the intervals where f(x) is concave up or concave down, and state the x-coordinate for the inflection point if it exists. Show all work
11. given f(x)=x3-4x2+5x-2 a.) State the y-intercept b.) Use the first derivative test, find all critical values, state the intervals where f(x) is increasing and any local maximum or minimum values for x. Show all work. c.) Use the second derivative test, find all critical values, find the intervals where f(x) is concave up or concave down, and state the x-coordinate for the inflection point if it exists. Show all work
b.) Use the first derivative test, find all critical values, state the intervals where f(x) is increasing and any local maximum or minimum values for x. Show all work.
c.) Use the second derivative test, find all critical values, find the intervals where f(x) is concave up or concave down, and state the x-coordinate for the inflection point if it exists. Show all work.
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Transcribed Image Text:11)Given : f (x) =x' – 4x² +5x – 2
a) State the y-intercept
b) Use the first derivative test, find all critical values, state the intervals where f(x) is increasing and any
local maximum or minimum values for x. Show all required work.
c) Use the second derivative test, find all critical values, find the intervals where f(x) is concave up or
concave down, and state the x-coordinate for the inflection point if it exists. Show all required work.
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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