2.8 The Derivative as a Function

Question 1

if a function is increasing what should the sign of the derivative be?

Answer 1

positive

Question 2

if a function is decreasing what should the sign of the derivative be?

Answer 2

negative

Question 2

what does a positive slope look like?

Answer 2

line going from bottom left to top right

climbing up the mountain

Question 3

when is a function not continuous?

Answer 3

at cusp, points, verticle tangents

Question 4

how to find f’(7) for example on a graph?

Answer 4

1. locate the point on the graph and draw a tangent line at the point
2. pick two points on the tangent line
   3.find the rise over run of the tangent line

Question 4

what does a negative slope look like?

Answer 4

line going from top left to bottom right

climbing down the mountain

Question 5

where does the derivative not exist

Answer 5

at a discontinuity like a hole or a corner

Question 6

how do find the graph derivative of a function when given the graph of the original function?

Answer 6

1. note where the max and min points are and plot them on the x-axis
2. wherever the function has a negative slope, will be below the x-axis or negative x values, and wherever the function has a positive slope will be above the x-axis positive x values

Question 6

what is a jerk?

Answer 6

the third derivative (of the initial function)

Question 6

a graph has four functions representing the position, velocity, acceleration, and jerk. identify the graphs

Answer 6

look at the points on each graph where there are horizontal tangents and see which other hits the axis at this point