The Relationship Between Increasing F'(X) And Positive F”(X) – Exploring The Concave Up Graph Of F(X)

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

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

If f'(x) is increasing, then it means that the slope of the tangent line at any point on the graph of f(x) is increasing. In other words, as x moves from left to right, the slope of the tangent line is getting larger.

Now, the derivative of f'(x) is f”(x), which is the second derivative of f(x). The second derivative of a function gives us information about the rate of change of the slope of the tangent line, or the concavity of the graph of the function.

So, if f'(x) is increasing, it means that the slope of the tangent line is getting larger. Therefore, f”(x) must be positive. In other words, the graph of f(x) is concave up.

To summarize: if f'(x) is increasing, then f”(x) is positive, and the graph of f(x) is concave up.

More Answers:
The Difference Quotient: An Alternate Definition Of Derivative In Calculus Mathematics.
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