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Determine the extrema on the given interval.$$f(x)=3 x+9 \text { on: }(a)[-1,3] ;(b)(-1,3)$$

(a) $\mathrm{M}=18, \mathrm{m}=6$(b) None

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 1

Extrema of a Function

Derivatives

Harvey Mudd College

University of Nottingham

Idaho State University

Lectures

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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01:55

01:14

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01:19

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07:11

03:18

Yeah. First we want to find the critical point of this function. Yeah. I take the rabbit house to this function. It's parameter was just three enhance. It cannot be their role of future events. Therefore we're just evaluates the function value at the boundary of the intraday for part A. The interval is from minus 123 and The functional value at -16 Function radio are three is 18, so six as A minimum and 18 is a maximum for part B. It's still the interval from miners want to scrape that. It is an opening drum, which means we cannot take the value -1 House right here. I use the arrow to illustrate this and the function value can Approach six or aging but it cannot reach and so there is no minimal and there's no maximum other

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