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

Question

f'(x) <0
f'(x)>0
f"(x) <0
f"(x) >0

Answer 1

the line must lie above the curve, so the graph must be concave down.
So, what do you think?

Answer 2

f"(x) < 0 ???????

Answer 3

right

Answer 4

but I posted this answer in my homework and the teacher marked (zero). I don't know what happened

Answer 5

I can not imagine what happened but agree that the second derivative is negative.