(b)(c)(d)AB/BC 5.
(b)The slopes are given in the table below. Be sure that the
segments you draw are correct relative to the other slopes in
the slope field with respect to the steepness of the segments.The solution curves will be concave down when .(−1,0) is a critical point because . And
, so by the second derivative test,
the solution curve f(x) has a local minimum.
m is the slope so replace into the differential equation:m = x − 2(mx + b) + 1 = (1 − 2m) x + (1 − 2b)
1 − 2m = 0 and 1 − 2b = m, so m = and b = .(a) The volume of the cord is V = πr^2 h. Differentiate with respect to
time, then substitute known values. (Be sure to use consistent units;
here, all measurements have been converted to inches.)Let θ represent the angle of elevation and h the height, as
shown.