Differentiation Assignment.sagews

Differentiation Assignment

Question 0

Watch the lecture video here.

Did you watch the video? [Type yes or no.]

Question 1

Consider the function $f(x)=e^x(x+2)^8$. Compute the following. [Remember, $e$ is not a variable.]

Part a

$f'(x)$

Part b

$f^{(4)}(x)$

Part c

$f''(3)$

Part d

$f^{(5)}(-4)$

Question 2

A ball is thrown straight up. The height of the ball (in feet) $t$ seconds after being thrown is given by $h(t)=-16t^2+20t+50$.

Part a

What is the velocity of the ball at $t=2$ seconds?

Part b

What is the acceleration of the ball at $t=2$ seconds?

Question 3

Find an equation of the tangent line of the function $g(x)=\dfrac{x}{x^{2}-4}$ at $x=1$.

Graph the function (in blue) and the tangent line (in red) on the same set of axes with $0.5 < x < 1.5$.

This material was developed by Aaron Tresham at the University of Hawaii at Hilo and is
licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.