Find the slope of the graph of the function at the given value. $f ( x ) = 4 ( 5 x + 6 ) ^ { 2 }$ at $x = 3$
A) $f ^ { t } ( 3 ) = 840$
B) $f ^ { t } ( 3 ) = 360$
C) $f ^ { t } ( 3 ) = 42$
D) $f ^ { t } ( 3 ) = 168$
E) $f ^ { t } ( 3 ) = 210$

Question

Quizplus · Accepted Answer

To find the slope of the graph of the function at $x = 3$, we need to find the derivative of the function and then substitute $x = 3$ into the derivative. The derivative of $f(x) = 4(5x + 6)^2$ using the chain rule is $f'(x) = 4 \cdot 2(5x + 6) \cdot 5 = 40(5x + 6)$. Substituting $x = 3$ gives $f'(3) = 40(5(3) + 6) = 40(15 + 6) = 40 \cdot 21 = 840$.

Find the Slope of the Graph of the Function at the Given