$\bf f(x)=ln(x-5)\qquad [6,8]\qquad \cfrac{df}{dx}=\cfrac{1}{x-5}\\\\
-----------------------------\\\\
\textit{mean value theorem}\qquad f'(c)=\cfrac{f(b)-f(a)}{b-a}\\\\
-----------------------------\\\\
f'(c)=\cfrac{1}{c-5}\qquad thus\quad \cfrac{1}{c-5}=\cfrac{f(8)-f(6)}{8-6}
\\\\\\
\cfrac{1}{c-5}=\cfrac{ln(3)-ln(1)}{2}\implies \cfrac{1}{c-5}=\cfrac{ln(3)-0}{2}
\\\\\\
\cfrac{2}{ln(3)}=c-5\implies \boxed{\cfrac{2}{ln(3)}+5=c}$

7 0

3 years ago

The graph of y = tan ⁡(x − π / 2) compared to the graph of y = tan ⁡x has:

vodomira [7]

Answer:

Last Option moved $\frac{\pi}{2}$ units right

Step-by-step explanation:

If we have a function f(x) and we want to move it horizontally then we make the transformation:

$y = f (x + h)$

If $h$ then the graph of f(x) moves horizontally h units to the right

If $h> 0$ then the graph of f(x) moves horizontally h units to the left.

In this case we have the function $y = tan (x)$ and the transformation is performed to obtain $y = tan(x- \frac{\pi}{2})$

Notice that in this transformation

$h$

<u><em>Then the graph of $y = tan (x)$ moves horizontally $\frac{\pi}{2}$ to the right</em></u>

5 0

3 years ago

Explain how estimation helps you place the decimal point when multiplying 3.9 &5.3

kow [346]

3.9 and 5.3, when rounded off and mult. together, produce the product 20.
Thus, the decimal point must follow the first two digits of your answer, whether estimate or "exact."

3.9*5.3 = 20.67 by calculator.

6 0

3 years ago