Mathematics

Problem

(a) Define the derivative of a function

f(x)

at a point

x=a

using first principles. (b) Describe briefly what information the sign of

f'(a)

gives about the behaviour of the function near

x=a

. (c) Let

f(x)=\sin x

. Using your definition from part (a), state the value of

f'(0)

and interpret your answer with respect to the tangent at the origin.