jee-advanced 2019 Q7

jee-advanced · India · paper2 Stationary points and optimisation Find critical points and classify extrema of a given function

Let $f : \mathbb{R} \rightarrow \mathbb{R}$ be given by $f(x) = (x-1)(x-2)(x-5)$. Define $$F(x) = \int_0^x f(t)\,dt, \quad x > 0$$
Then which of the following options is/are correct?
(A) $F$ has a local minimum at $x = 1$
(B) $F$ has a local maximum at $x = 2$
(C) $F$ has two local maxima and one local minimum in $(0, \infty)$
(D) $F(x) \neq 0$ for all $x \in (0, 5)$

Let $f : \mathbb{R} \rightarrow \mathbb{R}$ be given by $f(x) = (x-1)(x-2)(x-5)$. Define
$$F(x) = \int_0^x f(t)\,dt, \quad x > 0$$

Then which of the following options is/are correct?

(A) $F$ has a local minimum at $x = 1$

(B) $F$ has a local maximum at $x = 2$

(C) $F$ has two local maxima and one local minimum in $(0, \infty)$

(D) $F(x) \neq 0$ for all $x \in (0, 5)$

Paper Questions

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