Finding coordinates

Question

Find the coordinates of the points, if any, where each function has a horizontal tangent line. 

a) f(x)= x^3-8x^2+5x+3

Answer 1

Horizontal tangent is the point, where f'(x)=0 and tangent is parallel to x-axis. The first derivative is 3x²-16x+5.

Solving equation

3x²-16x+5=0,you get x=1/3 and x=5, which are  the x-coordinates of the tangent point(s). Now we can find y-coordinates.

For x=1/3, f(1/3)=3.81481

For x=5, f(5)=-47

So, coordiantes are (1/3, 3.81) and (5, -47).

 

 

 

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