How do you determine the intervals on which function is concave up/down and find points of inflection for y=4x5−5x4?

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ayibangaixgo · Accepted Answer

Step 1y=4x5−5x4y′=20x4−20x3=20(x4−x3)y″=20(4x3−3x2)=20x2(4x−3)y&quot; is never undefined and y″=0 at x=0 and at x=34.Step 2Because 20x2 is always positive, the sign of y is the same as the sign of 4x−3 (or build a sign table of sign diagram or whatever you have learned to call it, for y&#039;&#039;).y&quot; is negative (so the graph of the function is concave down, for x&amp;lt;34 andy&quot; is posttive (so the graph of the function is concave up, for x&amp;gt;34The curve is concave down on the interval (−∞,34) and concave up on (34,∞).The int (34,−81128) is the only inflection point.

How do you determine the intervals on which

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