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f(x)=2x³-6x²+6x+5 find local maxima and local …

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f(x)=2x³-6x²+6x+5 find local maxima and local minima

Posted by Manisha Behera 1 year, 4 months ago

CBSE > Class 12 > Applied Mathematics

1 answers

Preeti Dabral 1 year, 4 months ago

We have
f (x) = 2x³ – 6x² + 6x + 5
or f ′(x) = 6x² – 12x + 6 = 6 (x – 1)²
Now, f ′(x) = 0
{tex}\Rightarrow{/tex} x = 1
Thus, x = 1 is the only critical point of f . We shall now examine this point for local maxima and/or local minima of f. Observe that f ′(x) {tex}\ge{/tex} 0, for all x {tex}\in{/tex} R and in particular f ′(x) > 0, for values close to 1, to the left and to the right of 1. Therefore, by first derivative test, the point x = 1 is neither a point of local maxima nor a point of local minima. Hence x = 1 is a point of inflexion.

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CBSE > Class 12 > Applied Mathematics