If the function is 
and f(4) − f(1) = f '(c)(4 − 1) then there is not any answer.
Given function is and f(4) − f(1) = f '(c)(4 − 1).
In this question we have to apply the mean value theorem, which says that given a secant line between points A and B, there is at least a point C that belongs to the curve and the derivative of that curve exists.
We begin by calculating f(2) and f(5):
f(2)=
f(2)=1
f(5)=
f(5)=1
And the slope of the function:
(x)=
(c)=0
Now,
=-2
=0
-2 is not equal to 0. So there is not any answer.
Hence if the function is and f(4) − f(1) = f '(c)(4 − 1) then there is not any answer.
Learn more about derivatives at brainly.com/question/23819325
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Anything else to the problem?
Answer:
1/5
Step-by-step explanation:
The constant of proportionality is the slope
y/x since the line goes through (0,0)
y=1 and x=5 at the point given
1/5
<h3>
Answer: Choice C</h3>
Work Shown:
So that's why the answer is choice C
The requirement that x is nonzero isn't technically necessary. The original expression simplifies to choice C even when x = 0 is the case. Also, we don't have issues such as division by zero errors that could arise. It's a bit curious why your teacher put in that condition.
Answer:
III
Step-by-step explanation:
A function must have 1 y value assigned to each x value.
