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UPSC NDA Math Model Paper 9

Question : 100 of 120

Marks: +1, -0

f( x )\; = \;2x^{3} - 3x^{2} - 12x + 6

Solution:

Given

f( x )\; = \;2x^{3} - 3x^{2} - 12x + 6

As we know that Point c from the domain of the function y = f(x) is called stationary point of the function y

= f(x) \text{ if } f'(c) = 0

First find

f'(x).

f'(x) = \;6x^{2} - \;6x - 12

Now,

f'(x) = 0

\Rightarrow 6x^{2} - 6x - 12 = 0

\Rightarrow (x - 2)(x + 1) = 0

⇒ x = 2 and x = - 1

∴ Stationary point of the function are 2 and -1

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