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Whats the average rate of change of change for

f(x)=x^2+2x-1 as x goes from 1 to 2? Then how do i find the equation to the secant line of f(x)?

 Oct 22, 2019
 #1
avatar+8858 
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Whats the average rate of change of change for

f(x)=x^2+2x-1 as x goes from 1 to 2? Then how do i find the equation to the secant line of f(x)?

 

Was ist die durchschnittliche Änderungsrate für
f (x) = x ^ 2 + 2x-1, wenn x von 1 nach 2 geht? Wie finde ich dann die Gleichung zur Sekantenlinie von f (x)?

 

\(f(x)=x^2+2x-1\)

 

\(y_1=1^2+2\cdot1-1=2\\ P_1(1,2)\)

\(y_2=2^2+2\cdot 2-1=7\\ P_2(2,7)\)

 

The average rate of change is

\( m_{1,2}=\frac{y_2-y_1}{x_2-x_1}=\frac{7-2}{2-1}=\color{blue}2.5\)

 

The equation to the secant line of f(x) is

\(f(x)=y=m(x-x_1)+y_1\)

\(F(x)=y=2.5(x-1)+2=2.5x-2.5+2\)

\(f(x)=y=2.5x-0.5\)

laugh  !

 Oct 22, 2019
 #2
avatar+681 
+1

Amazing explanation asinus!! wink

Nirvana  Oct 23, 2019

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