6. A function f(x) is concave on the interval [a,b] if a. The function is differ

Question

6. A function f(x) is concave on the interval [a,b] if a. The function is differentiable in any point of the interval [a,b] b. The (first order) derivative of the function f increases on the interval [a,b), i.e. if xi>x2 then f(xi)>f(x2) for any points xi, x2, belonging to the c. The second order derivative of the function fin the interval [a,b] is d. The second order derivative of the function f in the interval [a,b] is e. All of the above interval [a,b] positive for the concave upward function. negative for the concave upward function.

Explanation / Answer

Option (d ) is RIGHT

option c and d are contradictory thats why option e is elliminated

regarding option a --> function is differentiable for convex function too

example of convex function is f(x)=-x^4

thus f'' = -12x^2

now for any value of x either -ve or +ve we get f'' is negative

thus option d is right

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