Discover The Local Minima Of A Function With Calculus: F'(2) = 0 And F”(2) > 0

f'(2)=0 and f”(2)>0

x=2 is a relative minimum of f(x)

Given that f'(2) = 0 and f”(2) > 0. We can conclude that the function f has a local minima at x = 2.

Explanation:

f'(2) = 0 means that the slope of the function f at x = 2 is zero. This is an indication that the function is neither increasing nor decreasing at that point.

f”(2) > 0 means that the second derivative of the function f is positive at x = 2. This means that the function is concave up at that point, which further implies that it has a minimum at x = 2.

Therefore, we can say that f has a local minima at x = 2. This means that there is no point close to x = 2 which has a smaller output value than f(2). However, there could be other points far away from x = 2 that have smaller output values.

Note that this conclusion is only valid for a small neighborhood around x = 2. We cannot say anything about the global behavior of the function f based on these two derivatives. To analyze the global behavior of the function, we would need to know more information about its behavior at other points.

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