Extending Differentiation

Question

Find the coordinates of the stationary (critical) point of the curve with equation y=1/(x²+4) 

Answer 1

The stationary critical point occurs when  f'(x) = 0.  This is because a stationary line is horizontal.  The point lies on and is tangent to this horizontal line.

 

f(x) = (x² + 4)^-1

 

-2x(x² + 4)^-2 = 0

 

-2x / (x² + 4)² = 0

 

x = 0    is a critical value

 

f(0) is a critical point.