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.
-$$f ( x ) = - 4 x ^ { 2 } + 7 x \text { at } ( 5,65 )$$
A) $- 13$
B) 33
C) $- 33$
D) 3

Question

Quizplus · Accepted Answer

The slope of the tangent line to the graph at a given point can be found by taking the derivative of the function and evaluating it at the x-coordinate of the given point. The derivative of $f(x) = -4x^2 + 7x$ is $f'(x) = -8x + 7$. Evaluating this derivative at $x = 5$ gives $f'(5) = -8(5) + 7 = -40 + 7 = -33$.

Choose the One Alternative That Best Completes the Statement or Answers