Please state whether each statement is true or false, and if false please explain why
If f''(2) = 0, then the graph of f must have a point of inflection at x = 2.
1. y' = b cos(bx)
y" = -b^2 sin(bx)
Maxima or minima of y' occur when y" = 0, so 0 = -b^2 sin(bx)
so sin(bx) = 0 for a maximum slope of y, so bx = 0 or bx = pi.
If bx = 0 then x = 0 (assuming b<>0, which must be true or y = 0!). If x=0 then ...
This shows how to determine the truth of two statements regarding functions and differentiations.