The graph of y = 5x^4 – x^5 has a point of inflection at what point? (multiple choice)?

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A. (0,0) onlyB. (3,162) onlyC. (4,256) onlyD. (0,0) and (3,162) E. (0,0) and (4,256)

Major Spinka DVM · Accepted Answer

y = 5x^4 - x^5 y' = 20x^3 - 5x^4y'' = 20 (3 - x) x^2 An inflection point is a point on a curve at which the sign of the curvature (i.e., the concavity) changes. If f''(x) > 0 for all x in some interval I, then f(x) is concave up on I. Conversely, if f''(x) < 0 for all x in some interval I, then f(x) is concave down on I. Possible inflection points will be those points where the second derivative is zero or doesn’t exist. However, do not assume that just because the second derivative is zero or doesn’t exist, the point will be an inflection point. It will only be an inflection point if the concavity is different on both sides of the point.Candidates are x = 0 and x = 3 ........ by solving y'' = 0y''(0+ε) > 0 and y''(0-ε) > 0 ......... ⇒ not an inflectiony''(3+ε) < 0 and y''(3-ε) > 0 ......... ⇒ x = 3 is an inflection pointAnswer: B (3,162) only

Major Spinka DVM · Answer

C is the best answer. start up on the x axis at 0 and flow up 4 on the y axis. -2/3 is the slope intercept so which you will flow down 2 and to the best 3 by way of fact the three is advantageous.

Prof. Cristobal Welch

The graph of y = 5x^4 – x^5 has a point of inflection at what point? (multiple choice)?

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