Iff(3)=6 andf(3)=3, what does the tangent line approximation give as an approximation for

(a) f(3.1)

(b) f(3.01)

Suppose f(x) has derivativef(x). In this problem, we will discover the derivative of the functionCf(x), whenever C is some fixed constant.

First, suppose that f(x)=ax+b. Findf(x)(Hint: derivative is slope)

Using your answer to (a), find the derivative ofCf(x) if f(x)=ax+b.

(c) Now suppose f(x) is an arbitrary function. Based on your results to parts (a) and (b), what do you expect that the derivative ofCf(x) is (Enter all multiplications)?

f f(x)=ax+b and g(x)=cx+d, what is

f(x)

g(x)

What is the derivative of f(x)+g(x)

Find the derivatives of the following functions

f(x)=x^3

f(x)=2x^4

f(x)=7x^43x^2+1

f(x)=x^1

(x)=14x

f(x)=(2+3x)^2

f(x)=17+2^3

(x^2+1)^2

3x^2+3x