Based on experimental data, the function t(x) = -3(x − 4)3 + 10 models the temperature of a special substance after being placed in a freezer for x minutes . the inflection point of the graph marks the moment when the substance changes from a liquid to a solid.

using complete sentences in your written answer, explain to your fellow scientists how to find the inflection point of this function.

Finding the slope of the graph where it is zero.

Step-by-step explanation:

when a substance is changing its state, it does so without change in temperature.

The rate of change of temperature with time should be zero.

This means that to get the inflection point you you should equation the given equation to zero.

i.e.  T(x) = 0

    -3(x − 4)3 + 10 = 0

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

cretdit to source

70

step-by-step explanation: