Find an equation of the secant line containing (1, f(1)) and (2, f(2)).
-$$f ( x ) = x ^ { 3 } - x$$
A) $y = 6 x - 6$
B) $y = - 6 x + 6$
C) $y = 6 x + 6$
D) $y = - 6 x - 6$

Question

Quizplus · Accepted Answer

To find the equation of the secant line, first calculate the slope using the points (1, f(1)) and (2, f(2)). For $f(x) = x^3 - x$, $f(1) = 1^3 - 1 = 0$ and $f(2) = 2^3 - 2 = 6$. The slope $m = \frac{f(2) - f(1)}{2 - 1} = \frac{6 - 0}{1} = 6$. Using point-slope form with point (1, 0), $y - 0 = 6(x - 1)$, simplifying gives $y = 6x - 6$.

Find an Equation of the Secant Line Containing (1, F(1)) f(x)=x3−xf ( x ) = x ^ { 3 } - xf(x)=x3−x

Find an Equation of the Secant Line Containing (1, F(1)) $f ( x ) = x ^ { 3 } - x$