Sarah competes in a long jump competition.
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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.
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For this case we have the following system of equations:
Equating the equations we have:
To find the solutions we factor the equation. To do this, we look for two numbers that, when multiplied, result in -3 and when added, result in -2.
These numbers are: -3 and +1
Thus, the factored equation is:
Then, the solutions for the variable "x" are:
We find the solutions for the variable "y":
Thus, the solutions are:
ANswer: