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Let $f(x)=x^{-1 / 2}$ on the interval (0,1] . (a) Does $f$ satisfy the conditions of Theorem $1 ?$ (b) Does it have a maximum value? (c) Does it have a minimum value?

(a) No(b) No(c) Min at $(1.1),$ Yes 1

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 1

Extrema of a Function

Derivatives

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04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

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first yet reveal the theorem one. The extreme value theory. It says that if the function defined by Y equals F, it is continuous and the closed bounded interval. Then it changed both the maximum and minimum value on this intro here. The function is continuous but the interval is not closed. It does not include the boundary zero. Hence it does not satisfy the condition of theory works next. We want to find the extreme of the function on this interval. Well, first I want to find the critical point. We take the relatives to this function primaries equals my nurse are half adds to a power of three house and we can rewrite it as minus a half times one over X to power free house. Since its directive cannot be zero. If you count Morning feels triggers it, that is it is invented. And hence at echo zero is a critical number here. The critical number is also the boundary of this syndrome and the X goes to zero. The function value goes to infinite, and vignettes goes to one. The function value goes to one, but not that here X cannot reach their room, and so this function has no maximum, but it has a minimum, which is what.

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