Question

1.) For y = f ( x ), the __________ from x = a to x = a + h is ; ℎ ≠ 0.

2.) The derivative has various applications and interpretations, including:

1. For each \x in the domain of f ′, f ́ ( x ) is the __________ of the line tangent to the graph of f at the point ( x , f ( x ) ).
2. For each ]x in the domain of f ′, f ́ ( x ) is the _________ rate of change of y = f ( x ) with respect to x.
3. If f ( x ) is the position of a moving object at time x, then v = f ′ ( x ) is the ___________ of the object at that time.

3.) A derivative f ′ ( x ) exists whenever   exists.

If the limit does not exist at x = c, we say that the function f is __________ at x = c.

Answer 1

1.) For y = f ( x ), the limiting from x = a to x = a + h is ; ℎ ≠ 0.

2.) The derivative has various applications and interpretations, including:

1. For each \x in the domain of f ′, f ́ ( x ) is the slope of the line tangent to the graph of f at the point ( x , f ( x ) ).
2. For each ]x in the domain of f′, f'(x) is the measurement of rate of change of y = f ( x ) with respect to x.
3. If f ( x ) is the position of a moving object at time x, then v = f ′ ( x ) is the velocity of the object at that time.

3.) A derivative f′(x ) exists whenever exists.

If the limit does not exist at x = c, we say that the function f is discontinuous at x = c.