#### To determine

**To define:**

The derivative f’(a), and two ways of interpreting this number.

#### Answer

i) It is the derivative of tangent line

ii) It is calculated by finding the limit

#### Explanation

Definition:

The derivative of a function f is f’(a) and is denoted by,

f'a=limh→0fa+h-f(a)h= limx→afx-f(a)x-a

Interpretation,

Derivative at a point is a, slope of tangent line drawn at that point

m=y2-y1x2-x1

The equation of a tangent line is y=mx+c where c is y-intercept.

Another way is by finding limit given below, that is it is the change in value of f(x) as change in x is gets close to 0

f'a=limh→0fa+h-f(a)h= limx→afx-f(a)x-a