I guess the function is . Then
and
.
The derivative is , but there is no
such that
This doesn't contradict Rolle's theorem because does not exists. In other words,
is not differentiable on (-27, 27), so the conditions of Rolle's theorem are not met. (Looks like that would be the last option, or the second to last option if the last one is "Nothing can be concluded")
Please consult the "Calculations" section of this ans .
The information we're given is below :
As per given information , we can do the following :
Point - slope form looks like so :
y-y₁=m(x-x₁)
y-6=-1/3(x-3)
y-6=-1/3x+1
y=-1/3x+1+7
y=-1/3x+6
↑
Answer:
The value of x = -1 makes the denominator of the function equal to zero. That is why this value is not included in the domain of f(x)
Step-by-step explanation:
We have the following expression
Since the division between zero is not defined then the function f(x) can not include the values of x that make the denominator of the function zero.
Now we search that values of x make 0 the denominator factoring the polynomial
We need two numbers that when adding them get as a result -1 and when multiplying those numbers, obtain -2 as a result.
These numbers are -2 and 1
Then the factors are:
We do the same with the numerator
We need two numbers that when adding them get as a result 4 and when multiplying those numbers, obtain 3 as a result.
These numbers are 3 and 1
Then the factors are:
Therefore
Note that only if
So since is not included in the domain the function has a discontinuity in