First you must derive the equation to find the slope: y = x ^ 3 y '= 3x ^ 2 Then, for x = -2 we have the slope is: y '(- 2) = 3 (-2) ^ 2 = 12 Then the equation of the line with slope equal to 12 and passing through point (3,2) is: y = 12 (x-3) +2
The altitude will be the geometric mean of the lengths, so . The smaller leg is the hypotenuse of a right triangle sides 4 and so the usual trig cliche, hypotenuse 8.