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.
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.
- What are the absolute extrema of #f(x)=2x^2 - 8x + 6 in[0,4]#?
- How do you find the critical points to sketch the graph #g(x)=x^4-8x^2-10#?
- What are the local extrema, if any, of #f(x)= 120x^5 - 200x^3#?
- Is #f(x)=-2x^3-5x^2-6x-1# increasing or decreasing at #x=1#?
- In the following graph, how do you determine the value of c such that #lim_(x->c) f(x)# exists?

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