3. Let f(x) = x - r - 3x. Determine the interval(s) on which f(x) is increasing and the interval(s) on which f(x) is decreasing, and find the x coordinates of all local maxima and minima. Then determine the interval(s) on which f(x) is concave up and the interval(s) on which f(x) is concave down, and find the x coordinates of all inflection points.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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3. Let \( f(x) = x - 3x^{\frac{1}{3}} \). Determine the interval(s) on which \( f(x) \) is increasing and the interval(s) on which \( f(x) \) is decreasing, and find the \( x \) coordinates of all local maxima and minima. Then determine the interval(s) on which \( f(x) \) is concave up and the interval(s) on which \( f(x) \) is concave down, and find the \( x \) coordinates of all inflection points.
Transcribed Image Text:3. Let \( f(x) = x - 3x^{\frac{1}{3}} \). Determine the interval(s) on which \( f(x) \) is increasing and the interval(s) on which \( f(x) \) is decreasing, and find the \( x \) coordinates of all local maxima and minima. Then determine the interval(s) on which \( f(x) \) is concave up and the interval(s) on which \( f(x) \) is concave down, and find the \( x \) coordinates of all inflection points.
Expert Solution
Step 1: Explanation

To find the points of minima and maxima first we need to find the critical points of function by equating the first derivative to zero.

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