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(C) By definition,the derivative $f'(1)$ is the limit of the slope of the secant line passing through $P(1, 2)$ and $Q(s, f(s))$ as $s 	o 1$.The slop

Vedclass · Accepted Answer

$4$

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(C) By definition,the derivative $f'(1)$ is the limit of the slope of the secant line passing through $P(1, 2)$ and $Q(s, f(s))$ as $s 	o 1$.The slope of the secant line is given by the coefficient of $x$ in the equation $y = \left( \frac{s^2 + 2s - 3}{s - 1} ight) x - 1 - s$.Thus,$f'(1) = \lim_{s 	o 1} \frac{s^2 + 2s - 3}{s - 1}$.Simplifying the expression:$f'(1) = \lim_{s 	o 1} \frac{(s - 1)(s + 3)}{s - 1}$$f'(1) = \lim_{s 	o 1} (s + 3) = 1 + 3 = 4$.Therefore,the correct option is $C$.

The graph of function $f$ contains the points $P(1, 2)$ and $Q(s, r)$. The equation of the secant line through $P$ and $Q$ is $y = \left( \frac{s^2 + 2s - 3}{s - 1} \right) x - 1 - s$. The value of $f'(1)$ is:

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