A critical point of a function y = f(x) is a point (c, f(c)) on the graph of f(x) at which either the derivative is 0 (or) the derivative is not defined. Let us see how to find the critical points of a function by its definition and from a graph.
Critical Numbers of a Function What are the critical numbers of a function? Well, the critical numbers of a function are values of the function {eq}f(x) {/eq}, x=c, such that either {eq}f'(c)=0 {/eq} {eq}f'(c) {/eq} does not exist. This is to say that any point at...
How to Find the Maximum Value of a Function Let's work through an example to find the maximum value of a function: {eq}f(x) = -3x^2 + 6x + 4 {/eq} Because we are given the equation in the general form, we can find the critical point by first taking the derivative to give ...
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Stationary point of a function is a point where the derivative of a function is equal to zero and can be a minimum, maximum, or a point of inflection
Select the "graph" or "plot" function of your calculator. Observe that two graphs, one of the parabola and one of the line, are graphed on the display. Note that the line and the parabola intersect at the points (0,0) and (1,1). Write down that the solution set of the two equat...
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Systems are useless unless they fulfill a business function. The first thing we need to be clear about is how to articulate a business function in terms that can be quantified and translated into system requirements. In this example I will use a hypothetical WordPress site that is critical to...
Find h'(x) for the following function: h(x) = x^x Let f(x) = 3x + 2x^3. A) Define the "Newton quotient" for this function at the point x = a. B) Simplify this by canceling "h" from the numerator and the denominator, where possible. C) Find the limit of ...
Find the following limit: {eq}\lim_{y \to -3} \frac{2}{y + 8} {/eq} Limits: The limit represents the value that a function approaches as the function's input approach some given value. It is an open interval ofy, which containsa, but whereydoes not equala. It is commonl...