Home > Calculus > Identifying Stationary Points (Critical Points) for a Function

How do you find the critical numbers of #1/(t^2+3)#?

Answer 1

Charles Anctil

The on;y critical number is #0#.

#f(t) = 1/(t^2+3)#

#f'(t) = (-2t)/(t^2+3)^2#

#f'(t)# is never undefined and is #0# only at #t=0#

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Answer 2

William Abdalla

To find the critical numbers of ( \frac{1}{t^2 + 3} ), we first find the derivative of the function with respect to ( t ), and then set it equal to zero to solve for ( t ). The derivative of ( \frac{1}{t^2 + 3} ) is given by the quotient rule. After finding the derivative, we solve for ( t ) when the derivative equals zero. This gives us the critical numbers.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.