If f(3)=6 and f′(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 derivative f′(x). In this problem, we will discover the derivative of the function C×f(x), whenever C is some fixed constant.
First, suppose that f(x)=ax+b. Find f′(x)(Hint: derivative is slope)
Using your answer to (a), find the derivative of C×f(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 of C×f(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^4-3x^2+1
f(x)=x^-1
(x)=1-4x
f(x)=(2+3x)^2
f(x)=17+2^3
(x^2+1)^2
-3x^-2+3x