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

Is #f(x)=-x^2+3x-1# increasing or decreasing at #x=1#?

Answer 1

Emily Ammerman

f(x) is increasing at x = 1

Evaluate f'(a) to find out if a function is increasing or decreasing at x = a.

• At x = a, f(x) is increasing if f'(a) > 0.

• At x = a, f(x) is decreasing if f'(a) < 0.

#f(x)=-x^2+3x-1rArrf'(x)=-2x+3#

and #f'(1)=-2(1)+3=1#

f(x) is increasing at x = 1 graph{-x^2+3x-1 [-10, 10, -5, 5]} since f'(1) > 0.

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Answer 2

Charles Anctil

To determine whether ( f(x) = -x^2 + 3x - 1 ) is increasing or decreasing at ( x = 1 ), we evaluate the derivative of the function at that point.

First, find the derivative of ( f(x) ) with respect to ( x ): [ f'(x) = \frac{d}{dx}(-x^2 + 3x - 1) = -2x + 3 ]

Now, evaluate ( f'(1) ): [ f'(1) = -2(1) + 3 = 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.