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A continuous function k(x) has critical values at x = 3, * = 4 and x = 5 and the function values k (3), k(4) and k(5) are all defined. Using the second derivative 12 (x-3) (x-3, 6) (x - 6,4) 25 (x - 5) to analyse the concavity of k(x), it can be concluded that k(x) has: NOTE: Test the concavity of the function on either side of each critical value. Try to make a rough sketch of the function from the information given above. Remember that if the second derivative is undefined at x=5 but k(5) exists, then there is either a sharp or vertical point at x=5.

A continuous function k(x) has critical values at x = 3, * = 4 and x = 5 and the function values k (3), k(4) and k(5) are all defined. Using the second derivative 12 (x-3) (x-3, 6) (x - 6,4) 25 (x - 5) to analyse the concavity of k(x), it can be concluded that k(x) has: NOTE: Test the concavity of the function on either side of each critical value. Try to make a rough sketch of the function from the information given above. Remember that if the second derivative is undefined at x=5 but k(5) exists, then there is either a sharp or vertical point at x=5.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A continuous function k(x) has critical values at x = 3, * = 4 and x = 5 and the function values k(3), k(4) and k(5) are all defined. Using the second derivative 12 (x-3) (x-3, 6) (x − 6, 4) 25 k" (x) = (x - 5) to analyse the concavity of k(x), it can be concluded that k(x) has: NOTE: Test the concavity of the function on either side of each critical value. Try to make a rough sketch of the function from the information given above. Remember that if the second derivative is undefined at x=5 but k(5) exists, then there is either a sharp or vertical point at x=5. points of inflection at x= type your answer... and at x= and a relative type your answer... minimum at x= type your answer...
Transcribed Image Text:A continuous function k(x) has critical values at x = 3, * = 4 and x = 5 and the function values k(3), k(4) and k(5) are all defined. Using the second derivative 12 (x-3) (x-3, 6) (x − 6, 4) 25 k" (x) = (x - 5) to analyse the concavity of k(x), it can be concluded that k(x) has: NOTE: Test the concavity of the function on either side of each critical value. Try to make a rough sketch of the function from the information given above. Remember that if the second derivative is undefined at x=5 but k(5) exists, then there is either a sharp or vertical point at x=5. points of inflection at x= type your answer... and at x= and a relative type your answer... minimum at x= type your answer...
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