jee-advanced 2007 Q65

jee-advanced · India · paper1 Stationary points and optimisation Find critical points and classify extrema of a given function

Let $f(x) = 2x^3 - 3x^2 - 12x + 4$. Then
(A) $f$ has a local maximum at $x = -1$ and a local minimum at $x = 2$
(B) $f$ has a local minimum at $x = -1$ and a local maximum at $x = 2$
(C) $f$ has local minima at $x = -1$ and at $x = 2$
(D) $f$ has local maxima at $x = -1$ and at $x = 2$

Let $f(x) = 2x^3 - 3x^2 - 12x + 4$. Then\\
(A) $f$ has a local maximum at $x = -1$ and a local minimum at $x = 2$\\
(B) $f$ has a local minimum at $x = -1$ and a local maximum at $x = 2$\\
(C) $f$ has local minima at $x = -1$ and at $x = 2$\\
(D) $f$ has local maxima at $x = -1$ and at $x = 2$

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