# math

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

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1. (y z x2)

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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.

When you see list of results click on:

Calc101com Automatic Calculus,Linear Algebra and Polynomials

When page be open clik option: derivatives

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.

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

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3. One of solutions is obviously:

x=0

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