Consider the cubic function f :R→ R , ƒ (x)=(x-a)' (x-b) where a and b are real constants, and a +b а. Find f'(x) in terms of a and b, and state the coordinates of the maximum M and the minimum turning point N on the graph of y= f(xr). b. For what values of x is the graph of y = f(x) strictly increasing. c. Let P be the midpoint of the line joining the points M and N, show that the coordinate 2a+b 2(a-b) of the point P is given by P 3 and that the point P lies on the 27 graph of y = f(x).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Question 4
Consider the cubic function f : R → R , ƒ (x)=(x-a)' (x– b) where a and b are real constants,
and a +b
а.
Find f'(x) in terms of a and b, and state the coordinates of the maximum M and the
minimum turning point N on the graph of y= f(x).
b.
For what values of x is the graph of y= f (x) strictly increasing.
m
с.
Let P be the midpoint of the line joining the points M and N, show that the coordinate
2a+b 2(a-b)'
of the point P is given by P
3
and that the point P lies on the
27
graph of y = f (x).
Transcribed Image Text:Question 4 Consider the cubic function f : R → R , ƒ (x)=(x-a)' (x– b) where a and b are real constants, and a +b а. Find f'(x) in terms of a and b, and state the coordinates of the maximum M and the minimum turning point N on the graph of y= f(x). b. For what values of x is the graph of y= f (x) strictly increasing. m с. Let P be the midpoint of the line joining the points M and N, show that the coordinate 2a+b 2(a-b)' of the point P is given by P 3 and that the point P lies on the 27 graph of y = f (x).
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