Derivative Definition

Question 1

Difference Quotient

Answer 1

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

Question 2

F’(a) =

Answer 2

lim f(a+h) - f(a)/h 
h---> 0

Question 3

What is it called when a limit exist for a derivative at a?

Answer 3

F is differentiable at a

Question 4

What are some other names for derivatives?

Answer 4

1) the slope of a tangent line.
2) the slope of a curve y=f(x) at point (a, f(a))
3) Instantaneous rate of change y=f(x) at point (a, f(a))

Question 5

Where derivatives do not exist you see… {list three}

Answer 5

1. Discontinuities.
   2) Sharp corners or cusps
   3) Vertical Tangent Line

Question 6

Tangent line in point slope form

Answer 6

y–f(a)= F’(a)(x-a)

Question 7

Secant Line

Answer 7

A line which connects two points on a function

Question 8

Tangent line

Answer 8

The line which runs through the one point on the graph in question. The slope of which is the instantaneous rate of change or derivative of the function at that point.

Question 9

Derivative

Answer 9

The slope of a tangent line.