Question

Which of the following is NOT a valid definition of a derivative?

Answer 1

Answer:

C. f'(x) = lim(h→0) [(f(x+h) − f(x)) / h]

Step-by-step explanation:

The first derivative is the slope between two points as the distance between those points approaches 0.  Slope is Δy/Δx.  Choice D is a valid way to write the first derivative.  It is the slope between the points (x, f(x)) and (x+h, f(x+h)).  Choice C is not a valid definition.

Answer 2

Answer:

C

Step-by-step explanation:

It should be:

lim h--> 0

[f(x+h) - f(x)]/h

That is,

In place of f(h), there should have been f(x)