Find all critical values for the function

Question

Find all critical values for the function
f(r)=[(3r)/(6r^2+10)]

and then list them (separated by commas).

Answer 1

The critical values of this function will occur where f'(x) = 0 or where f'(x) is undefined. To find the derivative, you need to use the Quotient Rule. 

f'(x) = 6(5 - 3x²)/(6x² + 10)² The derivative is defined for all real x. The only time that the derivative will equal zero is when the numerator equals zero. 5 - 3x² = 0 5 = 3x² 5/3 = x² x = √(5/3) and - √(5/3)