Find the points where the tangent line is parallel to x-axis. x^3 + 3x +14

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embizze | High School Teacher | (Level 1) Educator Emeritus

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The slope of the tangent line to the curve parallel to the x-axis will be the point(s) where the first derivative is zero:

f(x)=x^3+3x+14

f'(x)=3x^2+3

f'(x)=0 ==>

3x^2+3=0

3x^2=-3

x^2=-1

There is no real solution for this, thus there is no tangent line to the given function parallel to the x-axis.

The graph:

Note that the function is increasing for all real x, so the first derivative is positive everywhere.

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