Choose the one alternative that best completes the statement or answers the question.
Find the slope of the tangent line to the graph at the given point.
-$$f ( x ) = 5 x ^ { 2 } + x \text { at } ( - 4,76 )$$
A) -14
B) -41
C) 6
D) -39

Question

Quizplus · Accepted Answer

To find the slope of the tangent line to the graph at the given point, we first need to find the derivative of the function, which represents the slope of the tangent line at any point $x$. The given function is $f(x) = 5x^2 + x$. The derivative of this function, $f'(x)$, is found by applying the power rule: $$f'(x) = d/dx(5x^2) + d/dx(x) = 10x + 1.$$ To find the slope at the point $(-4, 76)$, we substitute $x = -4$ into the derivative: $$f'(-4) = 10(-4) + 1 = -40 + 1 = -39.$$ Therefore, the slope of the tangent line at the point $(-4, 76)$ is -39.

Choose the One Alternative That Best Completes the Statement or Answers