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

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

By signing up, you agree to our Terms of Service and Privacy Policy

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 ).

By signing up, you agree to our Terms of Service and Privacy Policy

- How do you verify that the hypotheses of rolles theorem are right for #f(x)= x sqrt(x+2)# over the interval [2,4]?
- How do use the first derivative test to determine the local extrema #f(x) = x / (x^2+1)#?
- Is #f(x)=x-sqrt(x^3-3x)# increasing or decreasing at #x=2#?
- What are the extrema of #f(x) = 7e^x#?
- How to demonstrate that #sqrt(2)^(sqrt(3)-1)>sqrt(3)^(sqrt(2)-1)#?We know that #g:(1,+oo)->RR,g(x)=##(lnx)/(x-1)#,and #g# is decreasing.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7