Determine the points on the curve y=x^2(x^3-x)^2 where the tangent line is horizontal. Thx!

Answer 1

(y z x2)

Answer 2

The slope of the tangent line is equal to the first derivative.

You must find where is first derivative=0

In this case the tangent line is horizontal.

In google type: calc101

When you see list of results click on:

Calc101com Automatic Calculus,Linear Algebra and Polynomials

When page be open clik option: derivatives

When this page be open in rectacangle type your equation and click options
DO IT

You will see solution for first derivative.

Then in google type: equation solver

When you see list of results click on:

Equation Calculator & Solver-Algebra.help

When this page be open in rectacangle type expresion for firste derivatives=0 and click options solve.

If your expresion is:
x^2*(x^3-x)^2

First derivative is:
4(2x^7-3x^5+x^3)

In this case in equation solver type:
4(2x^7-3x^5+x^3)=0

and solutions is:

-1, -sqroot(2)/2, sqroot(2)/2, 1

Answer 3

One of solutions is obviously:

x=0