For $f ( x ) = - \frac { 3 } { \sqrt { x } }$ ,find the average rate of change of f (x)with respect to x as x changes from 144 to 145.Then use calculus to find the instantaneous rate of change at x = 144.Round your answer to six decimal places,if necessary.
A)Average rate of change: 0.000864; Instantaneous rate of change: 0.000868
B)Average rate of change: -0.000864; Instantaneous rate of change: 0.125
C)Average rate of change: 0.000864; Instantaneous rate of change: -0.125
D)Average rate of change: -0.000864; Instantaneous rate of change: 0.000868

Question

Quizplus · Accepted Answer

The average rate of change is the slope of the secant line connecting the points (144, f(144)) and (145, f(145)). The instantaneous rate of change is the slope of the tangent line at the point (144, f(144)).

For f(x)=−3xf ( x ) = - \frac { 3 } { \sqrt { x } }f(x)=−x​3​

For $f ( x ) = - \frac { 3 } { \sqrt { x } }$