'Relative minimum' presentation slideshows

CHAPTER 3 SECTION 3.4 CONCAVITY AND THE SECOND DERIVATIVE TEST

CHAPTER 3 SECTION 3.4 CONCAVITY AND THE SECOND DERIVATIVE TEST. Definition of Concavity and Figure 3.24. Sketch 4 graphs a)1 decreasing and concave up b)1 increasing and concave up, c)1 decreasing and concave down, d)1 increasing and concave down. y. y. x. x. b. a. y. y. x. x. d. c.

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Math 140

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Maxima and Minima of Functions

Maxima and Minima of Functions. Maxima and minima of functions occur where there is a change from increasing to decreasing, or vice versa. Maxima and Minima of Functions. Maxima and minima of functions occur where there is a change from increasing to decreasing, or vice versa. 4. -3.

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1.5 Analyzing Graphs of a Function

1.5 Analyzing Graphs of a Function. Objective. Use the Vertical Line Test for functions. Find the zeros of functions. Determine intervals on which functions are increasing or decreasing and determine relative maximum and relative minimum values of functions.

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What you will learn

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Trig/Pre-Calculus Opening Activity

Trig/Pre-Calculus Opening Activity. Write the domain of the following functions. Solve the following inequalities. y. x. 4. -4. Definition of Graph. The graph of a function f is the collection of ordered pairs ( x , f ( x )) where x is in the domain of f . .

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Aim: How can we classify relative extrema as either relative minimums or relative maximums?

Aim: How can we classify relative extrema as either relative minimums or relative maximums?. Do Now:. The height of a ball t seconds after it is thrown upward from a height of 32 feet and with an initial velocity of 48 feet per second. Verify that f (1) = f (2)

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Sketching Functions

Sketching Functions. We are now going to use the concepts in the previous sections to sketch a function, find all max and min ( relative and absolute ), and identify any inflection points. Sketching Functions.

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Lesson 4-3

Lesson 4-3. First and Second Derivative Test for Relative Extrema. Quiz. Homework Problem: Differentials 3-11 f(x) = x 5 Use differentials to estimate f(2.001) Reading questions: Where is the first derivative test performed to determine a relative extrema?

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Obtaining Information from Graphs

Obtaining Information from Graphs. You can obtain information about a function from its graph. At the right or left of a graph, you will find closed dots, open dots, or arrows. A closed dot indicates that the graph does not extend beyond this point and the point belongs to the graph.

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Calculus Chapter 4

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Relative Extrema

Relative Extrema. Lesson 5.5. Video Profits Revisited. Recall our Digitari manufacturer Cost and revenue functions C(x) = 4.8x - .0004x 2 0 ? x ? 2250 R(x) = 8.4x - .002x 2 0 ? x ? 2250 Cost, revenue, and profit functions. Maximum profit when

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Concavity and Second Derivative Test

Concavity and Second Derivative Test. Lesson 4.4. ?. Concavity. Concave UP Concave DOWN Inflection point: Where concavity changes. At inflection point slope reaches maximum positive value. After inflection point, slope becomes less positive. Slope starts negative.

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Section 3: Increasing & Decreasing functions & the first derivative test

Learning Target: I will determine if a function is increasing or decreasing and find extrema using the first derivative. Section 3: Increasing & Decreasing functions & the first derivative test. AP Exam Practice. A function, f, is increasing on an interval for any

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5.2 Polynomials, Linear Factors, and Zeros

5.2 Polynomials, Linear Factors, and Zeros . P288-292. Ex) Write the polynomial in factored form. The following statements are equivalent: (x-b) is a linear factor of P(x) b is a zero of y=P(x) b is a of P(x)=0 b is a solution of P(x)=0 b is an x-intercept of y=P(x).

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Objectives: Be able to determine where a function is concave upward or concave downward with the use of calculus.

Concavity and the 2nd Derivative Test. Objectives: Be able to determine where a function is concave upward or concave downward with the use of calculus. Be able to apply the second derivative test to find the relative extrema of a function. Critical Vocabulary:

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Logarithmic Functions

Logarithmic Functions . Categorized as Transcendental (Non-Algebraic) Functions Inverse of an Exponential Function Many real-life situations can be modeled using logarithmic functions, including: Earthquake Intensity Human Memory Pace of life in Large Cities.

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Chapter 3: Applications of Differentiation

Chapter 3: Applications of Differentiation. L3.3 Increasing / Decreasing Functions and the First Derivative Test . Increasing and Decreasing Functions. If for every x 1 < x 2 on an interval f(x 1 ) < f(x 2 ) , then f is increasing [as x?, f ? ]

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Objective: Identify even or odd functions.

Objective: Identify even or odd functions. . Warm up Describe where is the function increasing, decreasing or constant. What is the relative maximum? What is the relative minimum?. Example 1 Classify each function as symmetric w.r.t . y-axis, origin or neither.

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