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

Increasing.

First, divide the binomials to avoid using the tedious three-pronged product rule.

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

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

To find the derivative of ( f(x) ), we use the product rule:

[ f'(x) = (x - 2)'(2x - 3)(2x - 1) + (x - 2)(2x - 3)'(2x - 1) + (x - 2)(2x - 3)(2x - 1)' ]

[ f'(x) = (1)(2x - 3)(2x - 1) + (x - 2)(2)(2x - 1) + (x - 2)(2x - 3)(2) ]

[ f'(x) = 4x^2 - 10x + 3 ]

Now, evaluate ( f'(-2) ):

[ f'(-2) = 4(-2)^2 - 10(-2) + 3 ]

[ f'(-2) = 16 + 20 + 3 ]

[ f'(-2) = 39 ]

Since ( f'(-2) ) is positive, ( f(x) ) is increasing at ( x = -2 ).

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

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.

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.

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.

- How do you find the intervals of increasing and decreasing using the first derivative given #y=x^2-6x+8#?
- How do use the first derivative test to determine the local extrema #f(x) = (x+1)(x-3)^2#?
- Is #f(x)=-e^(x^2-3x+2) # increasing or decreasing at #x=0 #?
- Is #f(x)=1/(x-1)-1/(x+1)^2# increasing or decreasing at #x=0#?
- How do you determine all values of c that satisfy the conclusion of the mean value theorem on the interval [0,7] for #f(x)=1/((x+1)^6)#?

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