Experts Please Help. Thank you

Question

State the coordinates of the intercepts, stationary points, and the inflection point of p(x) = x (x^2-1)^2?

a. Number of x-intercepts give the x,y coordinates:

b. y-intercept: (?,?)

c. number of stationary points:

d. number of inflection points:

Answer 1

a) x intercepts are when y =x(x²-1)² = 0 It is already factored. set x = 0 and x²-1 = 0 to find 3 roots.

b) y intercept is y value when x=0 , so just sub in. BTW, the constant term in a polynomial is the y intercept.

c) In order to find critical points (stationary points) find dy/dx = 0 or find roots of the 1st derivative. You can multiply everything out and take derivative or use product rule and chain rule. Any point that has a nonzero second derivative and a zero 1st derivative is a min or max (local or global - in this case both are local as the function grows to +/- infinity for large x.

d) In order to find inflection points: find the roots of the second derivative. You will find three. If the first derivative is nonzero, you have an inflection point. If it is zero, you have to make sure that the 1st derivative changes sign (this is not an issue here).

Use desmos.com to plot function. You will see the obvious min/max and the 3 inflection points (change in curvature - 2nd derivative goes through zero.

Please consider a tutor.

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Answer 2

desmos.com/calculator/x9xqye9vvf

Be sure to pause the video, take some notes, and make sure you can duplicate the process.