Question

Consider the function $f(x) = \frac{1}{\sqrt{x^4 + 1}}$ (a) Give the exact $x$ value of a non-stationary inflection point (an inflection point which is not a critical point) 1 (b) Give an $x$ value where the function is increasing, but concave down. DNE (c) Give an $x$ value where the function is decreasing, but concave down. DNE (d) Give an $x$ value where the function is increasing, but concave up. -1 (e) Give an $x$ value where the function is decreasing, but concave up. 1

          Consider the function $f(x) = \frac{1}{\sqrt{x^4 + 1}}$
(a) Give the exact $x$ value of a non-stationary inflection point (an inflection point which is not a critical point)
1
(b) Give an $x$ value where the function is increasing, but concave down.
DNE
(c) Give an $x$ value where the function is decreasing, but concave down.
DNE
(d) Give an $x$ value where the function is increasing, but concave up.
-1
(e) Give an $x$ value where the function is decreasing, but concave up.
1

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Consider the function f(x) = (1)/(√(x^4 + 1))
(a) Give the exact x value of a non-stationary inflection point (an inflection point which is not a critical point)
1
(b) Give an x value where the function is increasing, but concave down.
DNE
(c) Give an x value where the function is decreasing, but concave down.
DNE
(d) Give an x value where the function is increasing, but concave up.
-1
(e) Give an x value where the function is decreasing, but concave up.
1

Added by Wendy Z.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vincenzo Zaccaro

08/20/2023

Step 1

To find the first derivative, we'll use the chain rule and the power rule: f'(x) = -1/2 * (x^4 + 1)^(-3/2) * 4x^3 = -2x^3 / (x^4 + 1)^(3/2) To find the second derivative, we'll differentiate f'(x) again: f''(x) = -2 * (3x^2 * (x^4 + 1)^(3/2) - x^3 * 3/2 * (x^4 + Show more…

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Consider the function f(x) = 1/(sqrt{x^4 + 1}) (a) Give the exact x value of a non-stationary inflection point (an inflection point which is not a critical point) ◻ (b) Give an x value where the function is increasing, but concave down. ◻ (c) Give an x value where the function is decreasing, but concave down. ◻ (d) Give an x value where the function is increasing, but concave up. ◻ (e) Give an x value where the function is decreasing, but concave up. ◻ Consider the function f(x) = 1/(sqrt{x^4 + 1}) (a) Give an x value where the function is increasing, but concave down. DNE (b) Give an x value where the function is decreasing, but concave down. DNE (c) Give an x value where the function is increasing, but concave up. (d) Give an x value where the function is decreasing, but concave up. 45

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