Linearization and approximation

Question

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

Options:

1. f '(x) < 0
2. f '(x) > 0
3. f "(x) < 0
4. f "(x) > 0

Answer 1

The tangent line approximation will be greater than or equal to the value of f(x) if the graph of y = f(x) is concave down.

So, f"(x) < 0.