For the following function, a) give the coordinates of any critical points and classify each point as a relative maximum, a relative minimum, or neither; b) identify intervals where the function is increasing or decreasing; c) give the coordinates of any points of inflection; d) identify intervals where the function is concave up or concave down, and e) sketch the graph. h(x)=x²-27x
For the following function, a) give the coordinates of any critical points and classify each point as a relative maximum, a relative minimum, or neither; b) identify intervals where the function is increasing or decreasing; c) give the coordinates of any points of inflection; d) identify intervals where the function is concave up or concave down, and e) sketch the graph. h(x)=x²-27x
For the following function, a) give the coordinates of any critical points and classify each point as a relative maximum, a relative minimum, or neither; b) identify intervals where the function is increasing or decreasing; c) give the coordinates of any points of inflection; d) identify intervals where the function is concave up or concave down, and e) sketch the graph. h(x)=x²-27x
Show how you found the relative extreme values using Calculus based methods. a. Show how you found the critical point(s). b. Clearly identify how you determined whether a critical point was a relative maximum, relative minimum, or neither b providing evidence c. Make sure to show the check values you used to test whether the function is increasing or decreasing over each of the indicated subintervals.
Transcribed Image Text:For the following function, a) give the coordinates of any critical points and classify each point a sa relative maximum, a relative minimum, or neither; b) identify intervals where the function is increasing
or decreasing; c) give the coordinates of any points of inflection; d) identify intervals where the function is concave up or concave down, and e) sketch the graph.
h(x)=x²-27x
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a) What are the coordinates of the relative extrema? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
O A. The relative minimum point(s) is/are and the relative maximum point(s) is/are
(Simplify your answers. Use integers or fractions for any numbers in the expression. Type an ordered pair. Use a comma separate answers as needed.)
OB. The relative minimum point(s) is/are and there are no relative maximum point(s).
(Simplify your answer. Use integers or
fractions for any numbers in the expression. Type an ordered pair. Use a comma to separate answers as needed.)
O C. The relative maximum point(s) is/are and there are no relative minimum point(s).
(Simplify your answer. Use integers or fractions for any numbers in the expression. Type an ordered pair. Use a comma to separate answers as needed.)
O D. There are no relative minimum points and there are no relative maximum points.
b) On what interval(s) is h increasing or decreasing? Select the correct choice below and, necessary, fill in the answer box(es) to complete your choice.
O A. The function is increasing on. The function is decreasing on.
(Simplify your answers. Type your answers interval notation. Use a comma to separate answers as needed.)
OB.
The function is decreasing on. The function is never increasing.
(Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.)
O C. The function is increasing on. The function is never decreasing.
(Simplify your answer. Type your answer in interval notation. Use comma to separate answers as needed.)
O D. The function is never increasing or decreasing.
c) What are the coordinates of the inflection point(s)? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The coordinates of the inflection point(s) are.
(Simplify your answer. Type an ordered pair. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
There are no inflection points.
O B.
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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