calculus Flashcards
1
Q
what are the steps to draw a graph of f’(x) from a given drawn graph of f(x)
A
- label each turning point A, B, C, etc
- Identify if the slope of the graph is increasing or decreasing up to A
- If the slope is increasing, draw a curved line coming down to meet at A on the x-axis. (Increasing slope = y-values of f’(x) = +)
- If the slope is decreasing, draw a curved line coming up to meet at A on the x-axis. (decreasing slope = y-values of f’(x) = -)
- identify and draw the lines for the slopes between A and B, B and C, and so on
2
Q
what are the steps to draw a graph of f(x) from a given drawn graph of f’(x)
A
- label each root A, B, C, etc
- Identify if the y-values are positive or negative, leading up to root A
- If they are positive, your line will be an increasing slope, and stop to have a turning point at (A, x)
- If they are negative, your line will be a decreasing slope, and have a turning point at (A,-x)
- identify and draw the lines for the slopes between A and B, B and C, and so on
NOTE: the turning points will not be at (A,0), they will be somewhere on the line x=A. Since its a ‘sketch’ it doesnt matter where on that line, but make it appropriate, and not dramatically high or low
3
Q
what does ‘concave down’ mean
A
where the graph curves downwards
4
Q
what does ‘concave up’ mean
A
when f’’(x) > 0
5
Q
does a maximum on a y = f’ (x) graph go from + to - or - to +?
A
+ to -
6
Q
does a minimum on a y = f’ (x) graph go from + to - or - to +?
A
- to +
7
Q
what do you derive to get v(t)?
A
s(t)
8
Q
what do you derive to get a(t)?
A
v(t)