5/8 is the answer to this question
Answer:
The difference quotient for
is
.
Step-by-step explanation:
The difference quotient is a formula that computes the slope of the secant line through two points on the graph of <em>f</em>. These are the points with x-coordinates x and x + h. The difference quotient is used in the definition the derivative and it is given by

So, for the function
the difference quotient is:
To find
, plug
instead of 

Finally,


The difference quotient for
is
.
The value of K for which f(x) is a valid probability density function is 1/4.
<h3>How to solve for the value of K</h3>


![K[\frac{2^2}{2} -0]+[K[4(4-2)-(\frac{4^2}{2} -\frac{2^2}{2} )]=1](https://tex.z-dn.net/?f=K%5B%5Cfrac%7B2%5E2%7D%7B2%7D%20-0%5D%2B%5BK%5B4%284-2%29-%28%5Cfrac%7B4%5E2%7D%7B2%7D%20-%5Cfrac%7B2%5E2%7D%7B2%7D%20%29%5D%3D1)
open the equation
![K\frac{4}{2}+K[8 - (\frac{16}{2} -\frac{4}{2} )] = 1\\](https://tex.z-dn.net/?f=K%5Cfrac%7B4%7D%7B2%7D%2BK%5B8%20-%20%28%5Cfrac%7B16%7D%7B2%7D%20%20-%5Cfrac%7B4%7D%7B2%7D%20%29%5D%20%3D%201%5C%5C)
![2K+K[\frac{4}{2} ]=1](https://tex.z-dn.net/?f=2K%2BK%5B%5Cfrac%7B4%7D%7B2%7D%20%5D%3D1)
2K + 2K = 1
4K = 1
divide through by 4
K = 1/4
Read more on probability density function here
brainly.com/question/15714810
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Answer:
is the function of the least degree has the real coefficients and the leading coefficients of 1 and with the zeros -1, 5, and 2.
Step-by-step explanation:
Given the function

As the highest power of the x-variable is 3 with the leading coefficients of 1.
- So, it is clear that the polynomial function of the least degree has the real coefficients and the leading coefficients of 1.
solving to get the zeros

∵ 
as

so
Using the zero factor principle
if 


Therefore, the zeros of the function are:

is the function of the least degree has the real coefficients and the leading coefficients of 1 and with the zeros -1, 5, and 2.
Therefore, the last option is true.

From there we can see that because x equals both to a and b, it must be that a = b.