Solved on Sep 28, 2023
The derivative represents the instantaneous rate of change of at . This is the slope of the tangent line to at . True or False?
STEP 1
Assumptions1. The derivative is the instantaneous rate of change of with respect to when . . The instantaneous rate of change is the slope of the secant line to at the point .
STEP 2
The derivative of a function at a particular point is defined as the slope of the tangent line to the function at that point, not the secant line. The secant line is a line that connects two points on the function. When these two points get infinitely close, the secant line becomes a tangent line.
STEP 3
Therefore, the statement "The instantaneous rate of change is the slope of the secant line to at the point " is false. The correct statement should be "The instantaneous rate of change is the slope of the tangent line to at the point ".
The answer is False.
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