Description
0.36x^3 - 0.84x^2 + 5.52x - 6.84 = 0
And the inflection point from this second derivative:
y``= 0.107x^2 - 1.68x + 5.52
Explanation & Answer
You cannot find a min and max from the first equation. If you take the left hand side as a function, we can find a min and max. First you set the derivative equal to 0. This gives a quadratic equation that you can solve to find the relative min/maxes.
Inflection points are points where the 2nd derivative changes sign. Thus the 2nd derivative is 0 at that point. So you have to check both solutions of your quadratic second derivative. Looking at a parabola, if there really are two 0s of the second derivative then they both represent sign changes of the second derivative.
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