Define Sx to be the slope of the line through the points 0 0

Define S(x) to be the slope of the line through the points (0, 0) and (x, f(x)) based on the graph of f shown. At what value of x is S(x) minimum? At what value of x is S(x) maximum?

Solution

a) slope s(x) will be minimum at x = 8 (as it is the bottommost point the tangent at which through origin does not intersect the curve at any othre point)

b) slope s(x) will be maximum at x = 2  (as it is the topmost point the tangent at which through origin does not intersect the curve at any othre point)