Home > Calculus > Interpreting the Sign of the First Derivative (Increasing and Decreasing Functions)

Is #f(x)=x^2-x# increasing or decreasing at #x=1#?

Answer 1

Ezra Adams

#f(x)# is increasing at #x=1#

The slope of #f(x)# is given by the derivative of #f(x)#

#f'(x)=2x-1#

at #x=1) color(white)("X")f'(1)=1#

A slope #>0# implies that the function is increasing at this point.

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Answer 2

Emilia Aguilar

To determine if ( f(x) = x^2 - x ) is increasing or decreasing at ( x = 1 ), we evaluate the derivative of ( f(x) ) at ( x = 1 ).

The derivative of ( f(x) ) with respect to ( x ) is ( f'(x) = 2x - 1 ).

When ( x = 1 ), ( f'(1) = 2(1) - 1 = 1 ).

Since ( f'(1) > 0 ), the function is increasing at ( x = 1 ).

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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.