Question

Would it be A because if the local linear approximation is greater than or equal to the functions value its f''<0?



The function's value will always be greater than or equal to the local linear approximation of a function f if, for all x in an interval containing the point of tangency,

f " > 0
f " < 0
f ' > 0
f ' < 0

Answer 1

keep in mind that f '' (x) < 0 on some interval means f(x) is concave down on that interval

Answer 2

oh you said choice A, so you meant to say f '' (x) > 0 ?

Answer 3

Yes, @jim_thompson5910

Answer 4

choice A is correct

Answer 5

Thank you!