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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 2 years, 3 months ago

    CBSE > Class 12 > Applied Maths
    • 1 answers

    Preeti Dabral 2 years, 3 months ago

    We have
    f (x) = 2x3 – 6x2 + 6x + 5
    or f ′(x) = 6x2 – 12x + 6 = 6 (x – 1)2
    Now, f ′(x) = 0
    ⇒ 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) ≥ 0, for all x ∈ 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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