Question
Question: f : R → R be a differentiate function ∀ x ∈ R. If tangent drawn to the curve at any point x e (a, b)...
f : R → R be a differentiate function ∀ x ∈ R. If tangent drawn to the curve at any point x e (a, b) always lie below the curve then
A
f '(x) > 0, f "(x) < 0 ∀ x ∈ (a, b)
B
f '(x) < 0, f"(x) < 0 ∀ x ∈ (a, b)
C
f(x) > 0, f "(x) > 0 ∀ x ∈ (a, b)
D
None of these
Answer
f(x) > 0, f "(x) > 0 ∀ x ∈ (a, b)
Explanation
Solution
Tangents will lie below the graph if f '(x) increases with increase in x, i.e., f"(x) > 0.