Question
Asked Sep 23, 2019
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Find all the values of x where the tangent line is horizontal.
f(x) x3 -5x2-6x +7
X =
(Use a comma to separate answers as needed. Type an exact answer, using radicals as needed.)
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Find all the values of x where the tangent line is horizontal. f(x) x3 -5x2-6x +7 X = (Use a comma to separate answers as needed. Type an exact answer, using radicals as needed.)

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Expert Answer

Step 1

 Horizontal tangent line is located where the derivative of the function takes zero value.

 

Here the function is f (x) = x3-5x2-6x+7

 

For finding the value of x use the derivate of the function to locate the zero.

Step 2

Now the derivative of the function:

 

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f'(x)x5-6x+7) =3x2 -10x-6

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Step 3

Now for finding the value of x put f’(x) =0 .

 

3x2-10x-6=0

 

It’s a quadratic equation of the form ax2+bx+c =0 so the solutions are

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-btb -4ac х 3D 2а

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Tagged in

Math

Calculus