Learn How To Calculate The Second Derivative Of A Function And Determine Its Concavity With Critical Values

Find second derivativeFind critical valuesPositive – concave up, negative – concave down

Find where a function is concave down/up given an equation of f(x).

To find the second derivative of a function, we need to differentiate the first derivative of the function. Let’s say we have a function f(x). We can find the first derivative of f(x) as `f'(x)`. And the second derivative of f(x) can be calculated as `f”(x)`.

So, the steps to find the second derivative of a function are:

1. Find the first derivative of the function f(x), which is `f'(x)`.
2. Differentiate `f'(x)` to find the second derivative of f(x), which is `f”(x)`.

Once we have found the second derivative of the function, we can use it to determine the concavity of the function at different points.

To find the critical values of a function, we need to set the first derivative of the function equal to zero and solve for x. The values of x that we get after solving the equation are the critical values of the function.

If the second derivative of the function is positive at a critical value, the function is concave up at that point. If the second derivative is negative at a critical value, then the function is concave down.

To summarize:

1. To find the second derivative of a function f(x), differentiate the first derivative of f(x), which is `f'(x)`.
2. To find the critical values of a function, set the first derivative of the function equal to zero and solve for x.
3. If the second derivative of the function is positive at a critical value, the function is concave up at that point. If the second derivative is negative at a critical value, then the function is concave down.

More Answers: