Calculus 1-The Derivative of a Function Questions, guaranteed and verified 100%

1


The Derivative of a Function- HW Problems


1. Find the slope of the tangent line to the graph of the function at
the given point using a limit definition of a derivative.
𝑎. 𝑓 (𝑥 ) = 2𝑥 − 1 at (2,3)
𝑏. 𝑔(𝑥 ) = 𝑥 2 + 2𝑥 at (−1, −1)
𝑐. 𝑓 (𝑥 ) = 𝑥 3 at (1,1)
𝑑. 𝑓 (𝑥 ) = √𝑥 + 1 at (3,2)


2. Find an equation of the tangent line to the graph of the function at
the given point using a limit definition of the derivative.
𝑎. 𝑓 (𝑥 ) = 𝑥 3 at (1,1) (you can use the result from problem 1c)
2
𝑏. 𝑔(𝑥 ) = at (2,1)
𝑥
1
𝑐. 𝑓 (𝑥 ) = 2𝑥 − at (1,1)
𝑥



3. Calculate 𝑓′(𝑥) using a limit definition of a derivative. For what
values of 𝑥 does 𝑓′(𝑥) exist?
𝑎. 𝑓 (𝑥 ) = 2𝑥 2 − 𝑥
𝑏. 𝑔(𝑥 ) = 2𝑥 − 𝑥 3
1
𝑐. 𝑓 (𝑥 ) =
𝑥2

𝑑. 𝑔(𝑥 ) = √−1 − 3𝑥