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

What are the critical values of #f(x)=4x^2+2x+1#?

Answer 1

Charles Anctil

Polynomials are differentiable everywhere , so simply find where #f'(x)=0#

#f'(x)=8x+2=0#

critical value #=-1/4#

hope that helped

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Answer 2

Ezekiel Alexander

To find the critical values of ( f(x) = 4x^2 + 2x + 1 ), we need to find the derivative of the function and then solve for ( x ) when the derivative equals zero.

The derivative of ( f(x) ) is ( f'(x) = 8x + 2 ).

Setting ( f'(x) ) equal to zero and solving for ( x ), we get:

[ 8x + 2 = 0 ] [ 8x = -2 ] [ x = -\frac{2}{8} ] [ x = -\frac{1}{4} ]

So, the critical value of ( f(x) ) is ( x = -\frac{1}{4} ).

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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.