$\text { Find the slope } m \text { of the line tangent to the graph of the function } g ( x ) = 9 - x ^ { 2 } \text { at the }$ point $( 4 , - 7 )$
A) $m = 4$
B) $m = 9$
C) $m = - 8$
D) $m = - 7$
E) $m = - 18$

Question

Quizplus · Accepted Answer

To find the slope $m$ of the tangent line to the graph of $g(x) = 9 - x^2$ at a specific point, we need to compute the derivative of $g(x)$ with respect to $x$, which gives us the slope of the tangent line at any point $x$. The derivative of $g(x) = 9 - x^2$ with respect to $x$ is $g'(x) = -2x$. To find the slope at the point $(4, -7)$, we substitute $x = 4$ into $g'(x)$, yielding $g'(4) = -2(4) = -8$.

Find the slope m of the line tangent to the graph of the function g(x)=9−x2 at the \text { Find the slope } m \text { of the line tangent to the graph of the function } g ( x ) = 9 - x ^ { 2 } \text { at the } Find the slope m of the line tangent to the graph of the function g(x)=9−x2 at the

$\text { Find the slope } m \text { of the line tangent to the graph of the function } g ( x ) = 9 - x ^ { 2 } \text { at the }$