Show that the equation 4x3 + 2 = 5x2 + 2x has at least one solution...

Show that the equation 4x³ + 2 = 5x² + 2x has at least one solution on the interval [0,1]. Then, show that the equation has at most one solution on the interval [0,1]. Lastly, show that the equation has at exactly one solution on the interval [0,1].

Thanks for the help in advance!

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Expert Solution

The blue line in the last graph denotes y1.

Since the curves, y1=y2 at only one point between x=0 to x=1, hence it proves that the equation has at exactly one solution on the interval [0,1].

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milcah answered 1 year ago

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