Derivatives
Solve using the limit definition of a derivative
f(x)=5x^2+22x-4
10x+22
Find the derivative of
5sqrtx
5/(2sqrtx)
Find the average rate of change of the function on the interval [0,5].
f(x)=3x^2+8
15
The position of an object at any time t>0 is given below where t is in seconds and s is in meters.
A. What is the particle's position at time t=3 ?
s(t)=t^3-t^2-5t+2
5 meters
Derivative of:
-3/x^3
9/x^4
MOHLER MOMENT
Are you familiar with my culture?
1. Why's James cryin?
2. What's 9+10?
3. Happy Birthday Raven! "__ _______ _______."
4. Road work ahead.......
1. Cause he just got dunked on
2. 21
3. "I can't swim"
4. Uh, yeah. I sure hope it does.
Find the average rate of change of the function on the interval [0,7].
f(x)=3sqrt(x+9)
3/7
The position of an object at any time t>0 is given below where t is in seconds and s is in meters.
B. Is the object moving faster at t=1 sec or t=4 sec? Show your work.
s(t)=t^3-t^2-5t+2
v(1)=-4 m/s
v(4)=35 m/s
faster at 4 seconds
Find f'(x):
(-4x+3)(sqrtx)
(-4x+3)(1/2x^(-1/2))-4sqrtx
Find f'(1):
(x^2-3)/(7x)
4/7
Find the equation of the tangent line to the function when x=3
f(x)=5x^2-4x+1
y=26x-44
The position of an object at any time t>0 is given below where t is in seconds and s is in meters.
C. When is the object at rest (Hint available for -50 pts)?
s(t)=t^3-t^2-5t+2
5/3 seconds
Find f'(2):
f(x)=(3x-2x^2)^3
-60
Find the derivative:
root(3)(((x^2-1))^2
2/3(x^2-1)^(-1/3)(2x)
MOHLER MOMENT
1. What year did Mr. Mohler graduate high school?
2. What was Mr. Mohler's favorite Disney Channel show back in the day?
3. Would you still take my math class if I was a worm?
1. 2020
2. Good Luck Charlie
3. No. I couldn't teach if I were a worm.
The position of an object at any time t>0 is given below where t is in seconds and s is in meters.
D. When does the object have 0 acceleration?
s(t)=t^3-t^2-5t+2
1/3 seconds
Find f'(1):
((1-2x)/(1+x))^3
-9/16
Find the derivative:
(4x-x^2)^100(3x-1)
(4x-x^2)^100(3)+(3x-1)(100)(4x-x^2)^99(4x-2x)
Find the equation of the tangent line to the function when x=4
f(x)=15sqrt(x)
y=15/4x+15
The position of an object at any time t>0 is given below where t is in seconds and s is in meters.
E. What is the average rate of change of velocity on the interval [1,4]?
s(t)=t^3-t^2-5t+2
13 m/s^2