SOLUTION: Find an equation of the secant line containing (1, f(1)) and (2,f(2)). f(x) = x³ - x

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Question 431096: Find an equation of the secant line containing (1, f(1)) and (2,f(2)).
f(x) = x³ - x

Found 2 solutions by solver91311, Edwin McCravy:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


Substitute 1 for x in f(x)



Do the arithmetic to determine the value of f(1)

Repeat the process to determine the value of f(2)

Use the two-point form of an equation of a line to write the desired equation:



where and are the coordinates of the given points.


John

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Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!
Find an equation of the secant line containing (1, f(1)) and (2,f(2)).
f(x) = x³ - x


Let's calculate f(1)

f(x) = x³ - x
f(0) = 1³ - 1
f(0) = 0

So the point (1, f(1)) is the point (1,0)

Let's calculate f(2)

f(x) = x³ - x
f(2) = 2³ - 2
f(2) = 8 - 2
f(2) = 6

So the point (2, f(2)) is the point (2,6)

We plot those points:



Next we draw the graph (in red) and the secant line (in green):










That's the equation of the green secant line.

Edwin



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