Question
Asked Feb 21, 2020
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-3x? – x +1
1. Given g(x)=:
Determine
show algebraically that g'(x) =
2V#(x° +x+1}°
the x-value(s) of any horizontal tangents. *Hint: The domain of g(x) is important!
x² +x+1
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-3x? – x +1 1. Given g(x)=: Determine show algebraically that g'(x) = 2V#(x° +x+1}° the x-value(s) of any horizontal tangents. *Hint: The domain of g(x) is important! x² +x+1

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Expert Answer

Step 1

Given the function,

Calculus homework question answer, step 1, image 1

To calculate the derivative of function g(x), apply the quotient rule formula

Calculus homework question answer, step 1, image 2

Differentiate the function with respect to x

Calculus homework question answer, step 1, image 3

Step 2

The x values of any horizontal tangent,

Substitute the value of derivatives of function is equal to zero

Calculus homework question answer, step 2, image 1

Solve the quadratic equation for value x

 

Compare the equation with the standard equation,

Calculus homework question answer, step 2, image 2

Substitute the value of

Calculus homework question answer, step 2, image 3

 

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