How to find instantaneous rate of change for

hornejada1c 2022-07-03 Answered
How to find instantaneous rate of change for f ( x ) = e x at x=1?
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Answers (2)

grubijanebb
Answered 2022-07-04 Author has 10 answers
The instantaneous rate of change is also known as the derivative. It is analogous to the slope of the tangent line at a point, as well.
We might say that the instantaneous rate of change of f at x=a is equal to f'(a).
Here, we have to know that the derivative of e x is itself it's a unique and very important function, especially in calculus. That is:
f ( x ) = e x f ( x ) = e x
So, the instantaneous rate of change of f at x=1 is f'(1), and we see that:
f ( x ) = e x f ( 1 ) = e 1 = e
The instantaneous rate of change of f at x=1 is e, which is a transcendental number approximately equal to 2.7
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Aganippe76
Answered 2022-07-05 Author has 4 answers
Given:
f ( x ) = e x at x=1
d d x ( e x ) = e x
x=1
( d d x ( e x ) ) | ( x = 1 ) = ( e x ) | ( x = 1 ) = e
Answer:
f ( x ) = e x at x=1 is e
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