calculus

Question 1

what are the steps to draw a graph of f’(x) from a given drawn graph of f(x)

Answer 1

1. label each turning point A, B, C, etc
2. Identify if the slope of the graph is increasing or decreasing up to A
3. 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) = +)
4. 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) = -)
5. identify and draw the lines for the slopes between A and B, B and C, and so on

Question 2

what are the steps to draw a graph of f(x) from a given drawn graph of f’(x)

Answer 2

1. label each root A, B, C, etc
2. Identify if the y-values are positive or negative, leading up to root A
3. If they are positive, your line will be an increasing slope, and stop to have a turning point at (A, x)
4. If they are negative, your line will be a decreasing slope, and have a turning point at (A,-x)
5. 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

Question 3

what does ‘concave down’ mean

Answer 3

where the graph curves downwards

Question 4

what does ‘concave up’ mean

Answer 4

when f’’(x) > 0

Question 5

does a maximum on a y = f’ (x) graph go from + to - or - to +?

Answer 5

+ to -

Question 6

does a minimum on a y = f’ (x) graph go from + to - or - to +?

Answer 6

• to +

Question 7

what do you derive to get v(t)?

Answer 7

s(t)

Question 8

what do you derive to get a(t)?

Answer 8

v(t)

Question 9

what is the formula for the mean value (av(f)) of f(x) over the interval (a,b)?

Answer 9

av(f) = 1/(b-a) x the integral of f(x) from upper limit = b, to lower limit = a