Find all the points of local maxima and minima of the function. f(x) = x3 – 6x 2 + 9x – 8.
Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM
Let y = f (x) = x3 – 6x2 + 9 x – 8 Then,
=
= 3x2 – 12x + 9 = 3(x2 – 4x +3)
For a local maximum or local minimum, we have
= 0
3(x2 – 4x + 3) = 0
x= 1, 3.
We have to examine whether these points are points of local maximum or local minimum or neither of them.
We have, = 3(x – 1) (x – 3)
Clearly, changes sign from positive to negative as increases through 1.
x = 1 is a point of local maximum.
Also, changes sign from negative to positive as x increases through 3.
So x = 3 is a point of local minimum.
Answered by | 4th Jun, 2014, 03:23: PM
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