## Pages

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.