Find an equation of the tangent line to the graph of f at the given point. $f ( s ) = ( s - 5 ) \left( s ^ { 2 } - 3 \right),$ at $( 1,8 )$
A) $y = 10 s + 18$
B) $y = 2 s - 10$
C) $y = - 10 s - 2$
D) $y = - 10 s + 18$
E) $y = - 10 + 18 s$

Question

Quizplus · Accepted Answer

To find the tangent line, first find the derivative $f'(s)$ and evaluate it at $s=1$. The derivative is $f'(s) = 3s^2 - 10s + 15$. Evaluating at $s=1$, $f'(1) = -10$. The equation of the tangent line is $y - 8 = -10(s - 1)$, which simplifies to $y = -10s + 18$.

Find an Equation of the Tangent Line to the Graph f(s)=(s−5)(s2−3),f ( s ) = ( s - 5 ) \left( s ^ { 2 } - 3 \right),f(s)=(s−5)(s2−3),

Find an Equation of the Tangent Line to the Graph $f ( s ) = ( s - 5 ) \left( s ^ { 2 } - 3 \right),$