jackgartlqn said:Hi,
I have been going over past papers and i found this question. Find any local maxima or local minima of the functions g(x) = |f(x)| and h(x) = +√f(x) in the interval, −∞ < x < ∞.
How Would I go about solving this?
jackgartlqn said:Hi,
I have been going over past papers and i found this question. Find any local maxima or local minima of the functions g(x) = |f(x)| and h(x) = +√f(x) in the interval, −∞ < x < ∞.
How Would I go about solving this?
A local maximum or minimum of an undefined function is a point on the graph where the function has the highest or lowest value within a small interval of x-values. This means that there is no clear trend or direction for the function at that specific point.
To identify local maxima and minima of an undefined function, you can look for points on the graph where the derivative is equal to zero or does not exist. These points are called critical points and can indicate the location of local maxima and minima.
Yes, undefined functions can have multiple local maxima and minima. This occurs when the function has multiple critical points within a given interval.
You can use the first and second derivative tests to determine if a critical point is a local maximum, local minimum, or neither. The first derivative test involves evaluating the sign of the derivative on either side of the critical point, while the second derivative test involves evaluating the concavity of the function at the critical point.
Yes, there are other methods such as using a graphing calculator or plotting the function on a graph to visually identify local maxima and minima. You can also use numerical methods, such as the Newton-Raphson method, to approximate the locations of local maxima and minima.