Why F'(X) Being Increasing Implies That F”(X) Is Positive? | Explanation And Example

If f'(x) is increasing, then f”(x) is?

y-f(a)=f'(a)(x-a)

If f'(x) is increasing, then f”(x) is positive.

To explain this, let’s first define what it means for a function to be increasing. A function f(x) is said to be increasing on an interval if, for any two values a and b in that interval, f(a) < f(b) whenever a < b. Now, we know that the derivative f'(x) gives the rate of change of the original function f(x) at any given point. If the derivative is increasing, it means that the rate of change is increasing as well. This means that the slope of the tangent line to the curve of f(x) is becoming steeper as we move along the x-axis from left to right. If f'(x) is increasing, it implies that the slope of the tangent line is becoming steeper and steeper as we move along the x-axis. In other words, the second derivative of the function, f''(x), is positive. This is because the second derivative gives the rate of change of the first derivative (u = f'(x)). If the derivative of a function (f'(x)) is increasing, then its second derivative f''(x) is positive. Therefore, if f'(x) is increasing, we can conclude that f''(x) is positive.

More Answers: