Showing posts with label slope. Show all posts
Showing posts with label slope. Show all posts

Interactive: Derivative of Cosine

Derivative of the Sine Function: \[\frac{d}{{dx}}\left( {\cos x} \right) = - \sin x\]


Instructions: Drag P along \(f(x) = cos(x)\) to see that the slope of the tangent line through it traces out \(f'(x) = -sin(x)\).



Interactive: Derivative of Sine

Derivative of the Sine Function: \[\frac{d}{{dx}}\left( {\sin x} \right) = \cos x\]


Instructions: Drag P along \(f(x) = sin(x)\) to see that the slope of the tangent line through it traces out \(f'(x) = cos(x)\).



Interactive: Mean Value Theorem


Mean Value Theorem: Let \(f\) be a function that satisfies the following:
  • \(f\) is continuous on a closed interval \([a, b]\).
  • \(f\) is differentiable on the open interval \((a,b)\).
Then there is a number \(p\) in \((a,b)\) such that
\[f'\left( p \right) = \frac{{f\left( b \right) - f\left( a \right)}}{{b - a}}\]

Instructions: With the mouse, move points A and B along the function to see the Mean Value Theorem in action. Refresh browser to start over.




YouTube Video Lectures by Rob Shone

Interactive: Perpendicular Lines


Interactive Instructions: Move the green points to change m and see that perpendicular lines have opposite reciprocal slopes.



[ NOTESPerpendicular Lines ]


Interactive: Parallel Lines


Interactive Instructions: Move the green points to change m and see that parallel lines have the same slope. You can also move the orange line.


[ NOTESParallel Lines ]


Interactive: Slope-Intercept Form



Interactive Instructions: Slope-intercept form: y = mx + b. Move the green points to change m and b.





Interactive: Slope


Interactive Instructions:
Move the green points A and B.



Elementary Algebra Exam #2

Click on the 10 question exam covering topics in chapters 3 and 4. Give yourself one hour to try all of the problems and then come back and check your answers.


Graph. Also, find and label both the x- and y-intercepts.
 
Are the following lines parallel, perpendicular, or neither? Justify your answer.
 

Find the equation of the line:
 
 

  

 9. A light aircraft, flying with the wind, can travel 270 miles in 2 hours. On the return trip, flying against the same wind, the plane can only travel 210 miles in the same amount of time. What is the speed of the wind?
10. Marcia invested a total of 2,500 dollars in two separate accounts. One account earned 6% annual interest and the other earned 8%. If her total interest for the year was 167 dollars, then how much did she invest in each account?
 
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Intermediate Algebra Exam #1

Click on the 10 question exam covering topics in chapters 1 and 2. Give yourself one hour to try all of the problems and then come back and check your answers.






 



 

 
   
Solve and graph the solution set. In addition, express the solution set using interval notation.



Sketch the graph and give the domain and range.

  
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