Solved on Sep 28, 2023

The derivative f(a)f'(a) represents the instantaneous rate of change of f(x)f(x) at x=ax=a. This is the slope of the tangent line to f(x)f(x) at (a,f(a))(a, f(a)). True or False?

STEP 1

Assumptions1. The derivative f(a)f'(a) is the instantaneous rate of change of f(x)f(x) with respect to xx when x=ax=a. . The instantaneous rate of change is the slope of the secant line to f(x)f(x) at the point (a,f(a))(a, f(a)).

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 f(x)f(x) at the point (a,f(a))(a, f(a))" is false. The correct statement should be "The instantaneous rate of change is the slope of the tangent line to f(x)f(x) at the point (a,f(a))(a, f(a))".
The answer is False.

Was this helpful?
banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ContactInfluencer programPolicyTerms
TwitterInstagramFacebookTikTokDiscord