PreCalculus 3: Graphing Polynomial & Rational Fcts (19 of 29) Polynomials, Domain & Range, Factoring

In this video I will find the roots, domain and range, and graph y=2x^4-x^3+3x^2 by factoring (method 1).

Next video can be seen at:

[jamminermit]

At the end you have the range as being 378/256>=y>=-infinity, but shouldn’t you replace the >=-infinity with >-infinity as the y value can never equal -infinity?

[AliHasanAli]

Sir, you can not take the point in the exact half between the two roots and assume that it will give the max (min) value, because this is not correct at all (you can check it with some software and see that the range you found is not correct).
Instead, you can find the derivative of the original function, and find the zeros of the derivative. In this case, we are getting the points where the slope is zero (which means that they are either maximum values of minimum values).

[moviespoint]

if sin theta cos theta are roots of ax square plus bx plus c equal to zero then