Function Families are Family Fun! 😀 (Calculus Problems and Solutions)

#calculus #CalculusDerivatives #Mathematica

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(0:00) f(x)=x^3+a*x. How do the critical points and inflection points change as the parameter "a" changes? How does the graph change?
(7:28) f(x)=x^2+a/x. How do the critical points and inflection points change as the parameter "a" changes? How does the graph change?
(17:07) f(x)=a*x*e^(-b*x). How do the critical points and inflection points change as the parameters "a" and "b" change? How does the graph change?
(26:51) f(x)=e^(-a*x)*sin(b*x). How do the critical points change as the parameters "a" and "b" change? How does the graph change?

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[yisahak]

How to determine the rational root of fractional coefficient like ¼x⁴-2x³-½x³+½x²+2 and if constant term is 0 like ¼x⁴-2x³-½x³+½x²+2x