# Increase and decrease in functions

## Question 6: Given the function y=f(x). The function y = f'(x) has a graph as shown below. The function (g(x)=fleft(x^{2}+2 xright)-x^{2}-2 x) is covariate on which of the following intervals?

Question 6: Given the function y=f(x). The function y = f'(x) has a graph as shown below. The function (g(x)=fleft(x^{2}+2 xright)-x^{2}-2 x) is covariate on which of the following intervals? A. ((-1-sqrt{2} ;-1)) B. ((-1-sqrt{2} ;-1+sqrt{2})) C. ((-1 ;-1+sqrt{2})) D. ((-1 ;+infty)) (begin{array}{l} text { We have: } g(x)=fleft(x^{2}+2 xright)-x^{2}-2 x \ Rightarrow g^{prime}(x)=(2 x+2) …

## Question 7: Given the function f(x). The graph y=f'(x) is given as shown below. The function (g(x)=f(x-1)-frac{x^{2}}{2}) is inverse in which of the following ranges?

Question 7: Given the function f(x). The graph y=f'(x) is given as shown below. The function (g(x)=f(x-1)-frac{x^{2}}{2}) is inverse in which of the following ranges? A. (1 ; 3) B. (-2 ; 1) C. (2 ; 4) D. (0 ; 1) (begin{array}{l} text { We have: } g(x)=f(x-1)-frac{x^{2}}{2} Rightarrow g^{prime}( x)=f^{prime}(x-1)-x \ Rightarrow g^{prime}(x)=0 Leftrightarrow …

## Question 8: Given the function y=f(x) The function (y=f'(x)) has a graph as shown below. How many integer values ​​(m in .)[-10 ; 10]) so that the function (g(x)=f( 1-2 x+m)+x^{2}-(m+1) x+m^{2}) is inverse on the interval (1 ; 2 )

Question 8: Given the function y=f(x) The function (y=f'(x)) has a graph as shown below. How many integer values ​​(m in .)[-10 ; 10]) so that the function (g(x)=f( 1-2 x+m)+x^{2}-(m+1) x+m^{2}) is inverse on the interval (1 ; 2 ) A. 1 B. 2 C. 3 D. 4 (begin{array}{l} g^{prime}(x)=-2 f^{prime}(1-2 x+m)+2 xm-1, forall …

## Question 9: Given the function (f( x)=ax^{5}+bx^{4}+cx^{3}+dx^{2}+c x+f quad( a, b, c, d, c, f in mathbb{R})). Know that the graph of a function has a graph like the one shown below. Ask the function (g( x)=f (1-2 x)-2 x^{2}+1) covariate on which of the following intervals?

Question 9: Given the function (f( x)=ax^{5}+bx^{4}+cx^{3}+dx^{2}+c x+f quad( a, b, c, d, c, f in mathbb{R})). Know that the graph of a function has a graph like the one shown below. Ask the function (g( x)=f (1-2 x)-2 x^{2}+1) covariate on which of the following intervals? A. (left(-frac{3}{2} ;-1right)) B. ((-ten)) C. (((1;3)) D. …

## Question 10: Let the function y=f(x) be continuous on (mathbb{R}) and have a graph of the function (y=f'(x)) as shown below. On what interval is the function (g(x)=f(1-x)+frac{x^{2}}{2}-x) inverse?

Question 10: Let the function y=f(x) be continuous on (mathbb{R}) and have a graph of the function (y=f'(x)) as shown below. On what interval is the function (g(x)=f(1-x)+frac{x^{2}}{2}-x) inverse? A. (((1 ; 3)) B. ((-thirty first)) C. (left(-1 ; frac{3}{2}right)) D. ((-2 ; 0)) (begin{array}{l} g^{prime}(x)=-f^{prime}(1-x)+x-1, forall mathrm{x} in mathbb{R } \ g^{prime}(x)=-f^{prime}(1-x)+x-1 leq 0 …

## Question 48: The number of integer values ​​of m so that the function (y=frac{(2 m+1) x+3}{x+m}) is inverse on the interval (0;1) is

Question 48: The number of integer values ​​of m so that the function (y=frac{(2 m+1) x+3}{x+m}) is inverse on the interval (0;1) is A. 0 B. 1 C. 2 D. 3 (begin{array}{l} text { Defined set: } D=mathbb{R} backslash{-m} text { . }\ text { We have } y^{ prime}=frac{2 m^{2}+m-3}{(x+m)^{2}} text { . }\ …

## Question 49: Sum of integer values ​​of (m in[-25 ; 25]) so that the function (y=frac{(2 m+1) tan x+1}{tan x+m}) covariates over the interval (left(0 ; frac{pi} {2}right)) is

Question 49: Sum of integer values ​​of (m in[-25 ; 25]) so that the function (y=frac{(2 m+1) tan x+1}{tan x+m}) covariates over the interval (left(0 ; frac{pi} {2}right)) is A. 134 B. 217 C. 111 D. 325 (begin{array}{l} text { Definition: } tan x neq-m text { . }\ text { We have } y^{prime}=frac{2 …

## Question 50: Find the values ​​of m so that the function (y=frac{(2 m+1) tan x+1}{tan x+m}) covariates on the interval (left(0) ; frac{pi}{2}right)) is?

Question 50: Find the values ​​of m so that the function (y=frac{(2 m+1) tan x+1}{tan x+m}) covariates on the interval (left(0) ; frac{pi}{2}right)) is? A. (m>frac{1}{2}) B. (mgefrac{1}{2}) C. (m0) (begin{array}{l} text { Definition: } tan x neq-m text { . }\ text { We have } y^{prime}=frac{2 m^{2}+m-1}{cos ^{2} x(tan x+m)^{2}} text { . …

## Question 1: Number of integer values ​​of (m in[-25 ; 25]) so that the function (y=frac{(2 m+1) tan x+1}{tan x+m}) covariates over the interval (left(0 ; frac{pi} {2}right)) is:

Question 1: Number of integer values ​​of (m in[-25 ; 25]) so that the function (y=frac{(2 m+1) tan x+1}{tan x+m}) covariates over the interval (left(0 ; frac{pi} {2}right)) is: A. 15 B. 20 C. 25 D. 30 (begin{array}{l} text { Definition: } tan x neq-m text { . }\ text { We have } y^{prime}=frac{2 …

## Question 2: Given the function (y=frac{x+m^{2}}{x+1}) where m is the real parameter. Find all values ​​of m so that the function is inverse on each specified interval.

Question 2: Given the function (y=frac{x+m^{2}}{x+1}) where m is the real parameter. Find all values ​​of m so that the function is inverse on each specified interval. A. (min(-1;1)) B. (min(1;+infty)) C. (min(-infty;-1)) D. (m in(-infty ;-1) cup(1 ;+infty)) (begin{array}{l} text { Defined set: } D=mathbb{R} backslash{-1} text { . }\ text { We have …