Question

The function $f(x)$ is a polynomial and hence it is defined for all real numbers. Its second derivative is given by: $f''(x) = -5(x+3)(x-1)^2(x-2)$. Find the interval(s) over which the function $f(x)$ is concave up. $( -3, 1)$ and $(2, \infty)$ $( -\infty, -3)$ and $(1, \infty)$ $( -\infty, -3)$ and $(1, 2)$ $(-3, 2)$ $( -\infty, -3)$ and $(2, \infty)$ None of the above.

          The function $f(x)$ is a polynomial and hence it is defined for all real numbers. Its second derivative is given by: $f''(x) = -5(x+3)(x-1)^2(x-2)$. Find the interval(s) over which the function $f(x)$ is concave up.
$( -3, 1)$ and $(2, \infty)$
$( -\infty, -3)$ and $(1, \infty)$
$( -\infty, -3)$ and $(1, 2)$
$(-3, 2)$
$( -\infty, -3)$ and $(2, \infty)$
None of the above.

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The function f(x) is a polynomial and hence it is defined for all real numbers. Its second derivative is given by: f”(x) = -5(x+3)(x-1)^2(x-2). Find the interval(s) over which the function f(x) is concave up.
( -3, 1) and (2, ∞)
( -∞, -3) and (1, ∞)
( -∞, -3) and (1, 2)
(-3, 2)
( -∞, -3) and (2, ∞)
None of the above.

Added by Ruben G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

02/13/2023

Step 1

Step 1: To determine the intervals over which the function f(x) is concave up, we need to find the values of x for which the second derivative f''(x) is positive. Show more…

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Please answer right away, I'll leave a 5-star review if done within 40 minutes. The function f(x) is a polynomial and hence it is defined for all real numbers. Its second derivative is given by f''(x) = 5x + 3x^2. Find the intervals over which the function f(x) is concave up. A) -3,1 and 2 B) -3 and 1 C) -3 and 1.2 D) -3,2 E) -3 and 2 F) None of the above

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