If a function f(x) is convex at x = a, then f”(a) < 0.
If a function f(x) is convex at x = a, then f”(a) < 0.
The correct option is B False
In the interval in which a function is convex, the value of the derivative f’(x) keeps on increasing. So we can say f”(x) will be greater than than zero.
One example would be y = x2
The shape of this function is upward parabola. This is a typical example of a convex function. Here, as you can see from the graph, the slope of tangent increases as x increases. Initially the slope of the tangent (f’(x) ) is negative when x is negative and slope becomes zero at x =0. For positive values of x, the slope is positive. So we can say the slope or f’(x) increases as x increases. So the derivative of f’(x) which is f"(x) should be positive.
Any point on the x-axis would have f”(x) positive in case of convex function y = x2
False
In the interval in which a function is convex, the value of the derivative f’(x) keeps on increasing. So we can say f”(x) will be greater than than zero.
One example would be y = x2
The shape of this function is upward parabola. This is a typical example of a convex function. Here, as you can see from the graph, the slope of tangent increases as x increases. Initially the slope of the tangent (f’(x) ) is negative when x is negative and slope becomes zero at x =0. For positive values of x, the slope is positive. So we can say the slope or f’(x) increases as x increases. So the derivative of f’(x) which is f"(x) should be positive.
Any point on the x-axis would have f”(x) positive in case of convex function y = x2
