Calculate the differentiation

Calculate the differentiation of the logarithmic function

Find the points of local maxima, local minima and the points of inflection of the function

Quadratic function

If the sum of two consecutive 
numbers is $45$ and one number is $X$ 
.This statement in the form of 
equation $1s:$ 
$\left(1$ Point) $\right)$ 
$○5x+1$ $1eft\left(x+1$ $r1gnt\right)=45s$ 
$○sx+1ef\left(x+2$ $r1gnt\right)=145s$ 
$sx+1x=45s$ 

$s|ef\left(-1n$ $\left($ }\right)^{50}\ $\right)$ \ | | is\ equal\ to\ $S$ 
$s1S$ 
$S-1S$ 
$s2S$ 
$s50s$ 

The is the statement of the Mean Value Theorem from your $te\times tb00k$ 
$Tneoren$ $m4.5$ $Ne8n$ Value Theorem 
Let f be continuous over $leclose$ interval $\left(a.b\right)aod$ $i$ $eo$ $xd$ $csnlc$ $\left(ab\right)$ $mmd$ 
exists at least one point cE $\left(a.b\right)$ $si1dhtba$ 
$f^{'}\left(c\right)=\dfrac {f\left(b\right)-f\left(a\right)} {b-a}$ 
What is the geometric interpretation of the conclusion of the theorem? 
O The tangent line to the graph of $f\left(x\right)$ at $l\left(c1\right)$ is parallel to the 
secant line connecting $\left(a,f\left(a\right)\right)$ and 
$\left(b,f\left(b\right)\right)$. 
O The tangent line to the graph of $\left(f\left(lef\left(x\left(right\right)$ at $c$ is the secant line 
connecting $\left(a,f\left(a\right)\right)$ $ana$ $\left(b,f\left(b\right)\right)$. 
O The tangent line to the graph $of$ $\left(f\left(leF\left(x\left(right\right)\left(\right)at1\left(c1\right)is$ perpendicular to the 
secant line connecting $\left(a,f\left(a\right)\right)$ and 
A(\left(b,f\left(b\right)\right)\). 
O The tangent line to the graph of $\left(fleH\left(x\right)nght\right)\right)\right)$ $at$ $\left(c\right)\right)ishoizonta|$ 
$Tnere$ is more than one tangent line to the graph $0no$ $\left(flcf\left(x\right)night\right)\left($ $at1\left(c1\right)$ 


$\right)c$ $c$ $co$ $3c3x$ $x$ 
Question 2 $1pts$ 
For each of the following questions, clearly select the ONE correct 
answer. 
Which of the following functions is increasing on the interval $\left(0,1\right)7$ $Ap$ 
$Ass$ 
Coe 
$-lnlef\left(x\right)ngh$ Col 
$x-ln\left(x\right)$ $x-1$ 
$Co$ 
$○y$ $xcos\left(2x\right)$ Diff 
Eva 
$O-\dfrac {3x} {x-1}-1trac\left(3x\right)\left(x-1\right)$ Fac 
Inte 
$○x$ $x$ $ln\left(x\right)$ Lim 
Seri 
Sim 
Solu 
$Ne\times t$ > Con 
$Con$ 
$Con$ 

What is the inverse of $g\left(x\right)=\sqrt{x-1} $ 
$Og\left(x\right)=\sqrt{x+1} $ 
$+1$ $g^{'}\left(x\right)=5-$ $y_{9}$ $g\sqrt{ef\left(x\left(nght\right)} =\left(f_{tac\left(x+1\right)0sq\pi \left(x\right)}$ 
$Og^{'}\left(x\right)=x^{2}+1$ 
$○g\left(x\right)=x^{2}-1$ 
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