Find an equation for the tangent to the curve at the given point.
-$$f ( x ) = 10 \sqrt { x } - x + 3 , ( 100,3 )$$
A) $y = 3$
B) $y = - \frac { 1 } { 2 } x + 3$
C) $y = \frac { 1 } { 2 } x - 53$
D) $y = - \frac { 1 } { 2 } x + 53$

Question

Quizplus · Accepted Answer

To find the equation of the tangent line, we first need to find the derivative of the function: 
$$f'(x) = \frac{5}{\sqrt{x}} - 1$$
Then evaluate the derivative at x=100 to find the slope of the tangent line:
$$f'(100) = \frac{5}{\sqrt{100}} - 1 = 1$$
So the slope of the tangent line is 1. Using the point-slope form of the equation of a line, we have:
$$y - 3 = 1(x-100)$$
Simplifying, we get:
$$y = -\frac{1}{2}x + 53$$
Therefore, the correct answer is D.

Find an Equation for the Tangent to the Curve at the Given