Q. 12

# <span lang="EN-US

y = x4 – 2x3 + x2 + 3

y’ = 4x3 – 6x2 + 2x

At extrema of y, y’ = 0

i.e., 4x3 – 6x2 + 2x = 0

or, 2x3 – 3x2 + x = 0

x(2x – 1)(x – 1) = 0

i.e., x = 0, x = 1/2 and x = 1 correspond to extrema of y

Now, y’’ = 12x2 – 12x + 2

y’’0 = 2 > 0 x = 0 corresponds to a minima

y’’1/2 = -1 < 0 x = 1/2 corresponds to a maxima

y’’1 = 2 > 0 x = 1 corresponds to a minima

So, x = 0 and x = 1 are the ordinates we need.

So, the area A is –

A =

=

(Ans)

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