Question

The graph of the function $f$, shown at the right, has horizontal tangents at $x = -2, 0$, and 3. If the function $G$ is defined by $G(x) = int_{-4}^{x} f(t) dt$, for $-4 le x le 4$, which of the following statements about $G$ are true? I. $G$ is increasing on $(1, 2)$. II. $G$ is decreasing on $(-4, -3)$. III. $G(0) < 0$. (A) None (B) II only (C) II and III only (D) I, II, III

          The graph of the function $f$, shown at the right, has horizontal tangents at $x = -2, 0$, and 3. If the function $G$ is defined by
$G(x) = int_{-4}^{x} f(t) dt$, for $-4 le x le 4$, which of the following statements about $G$ are true?
I. $G$ is increasing on $(1, 2)$.
II. $G$ is decreasing on $(-4, -3)$.
III. $G(0) < 0$.
(A) None (B) II only (C) II and III only (D) I, II, III

The graph of the function f, shown at the right, has horizontal tangents at x = -2, 0, and 3. If the function G is defined by
G(x) = int-4^x f(t) dt, for -4 le x le 4, which of the following statements about G are true?
I. G is increasing on (1, 2).
II. G is decreasing on (-4, -3).
III. G(0) < 0.
(A) None (B) II only (C) II and III only (D) I, II, III

Added by Jose Maria M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vincenzo Zaccaro

05/01/2022

Step 1

Step 1: G is increasing on (1, 2) is false because the area under the curve from 1 to 2 is decreasing since the function f is negative in that interval. Show more…

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The graph of the function f, shown at the right, has horizontal tangents at x = -2, 0, and 3. If the function G is defined by G(x) = ∫_{-4}^{x} f(t) dt, for -4 ≤ x ≤ 4, which of the following statements about G are true? I. G is increasing on (1, 2). II. G is decreasing on (-4, -3). III. G(0) < 0. (A) None (B) II only (C) II and III only (D) I, II, III