J1в в в в в в в в нBBBBBBB45631 2X14-2 11 3f(x)92. The function f is twice differentiable. Selected values of f are given in the table above. Which of the followicould be the graph of f"(x), the second derivative of f?(A)(B)y(C)My food faX-X2 4 5 63 4 5 65/6(D)(E)1 2 3 4 5 6cs ScaNGUYENPerson Usage PurgaseU NGUYENcannero sise 440 8JEDIDIA "SOGUSS A SHINGOA

We can solve this using Newton divided differences method

Answered: B 4 3 5 6 1 -2 1 1 4 3 f(x) 1 92. The…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter8: Graphing Quadratic Functions

Section: Chapter Questions

Problem 17CT

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Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.
The definition of the derivative function is f′(x)=f(x+h)−f(x)h.f′(x)=h→0limhf(x+h)−f(x). Use this definition to calculate the derivative of f(x)=3x+1f(x)=3x+1. Show all work.
A thin observatory probe having the shape of a plate is probing a volcano in an xy −plane at a point P(x, y). The probe can only withstand a certain amount of temperature; thus, Represent the temperature as the function of x and y when the temperature calculated in degrees Celsius is inversely proportional to the square of its distance from theorigin.
Find the critical point of the function. Then use the second derivative test to classify the nature of this point, if possible. (If an answer does not exist, enter DNE.) f(x, y) = xy + 3 x + 9 y critical point (x, y) = classification       Finally, determine the relative extrema of the function. (If an answer does not exist, enter DNE.) relative minimum valuerelative maximum value
Derivative of function y=ln(9x3+5x)9/5 y'=9/5(9x3+5x)4/5X(27x2+5) Numerator (9x3+5) Denominator y'=9(9x3+5x)4/5X(27x2+5) Numerator 5 (9x3+5x)9/5   Denominator y'=9(27x2+5x) Numerator 5(9x3+5x) Denominator, =answer I am not understanding what math caused the second to last step to turn into the answer?
Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an answer does not exist, enter DNE.) f(x) = x2 + 5x − 3 relative maximum     (x, y) = relative minimum     (x, y) =
Find the absolute extrema of the function on the closed interval. Use a graphing utility to verify your results. (If an answer does not exist, enter DNE.) g(x) = 20(1+ 1/x + 1/x2 ), [−5, 5] Step 1: Begin by finding the derivative of g(x). Step 2: Find the critical numbers and points of discontinuity. (Enter your answers as a comma-separated list.) x = Step 4: Find the absolute extrema. (If an answer does not exist, enter DNE.) absolute maximum (x, y) = absolute minimum (x, y) =
a) Determine the domain of the function f (x) = √1 − x2. b) Calculate its derivative. Study the sign of the derivative f ′ (x) at x∈D (f). Construct a table with the sign of the derivative according to the value of x, the variations of (x) (increasing or decreasing). c) Enter in the table the value of that cancels f ′ (x), is it a minimum, or a local maximum, or absolute? Are the extremes of the domain minimum, or local maximum, or absolute?
4.The derivative of a function f is given by f'(x)=(-2x-2)e^x, and f(0) = 3.A. The function f has a critical point at x = -1. At this point, does f have a relative minimum, a relative maximum, or neither? Justify your answer.B. On what intervals, if any, is the graph of f both increasing and concave down? Explain your reasoning.C. Find the value of f(-1).
A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with dimensions 16cm by 30cm by cutting equal squares from the four corners and turning up the sides. State the formula for the volume of a rectangular prism (aka box). Express the volume formula as a function of x. What is the domain of V? Find the derivative of V(x) with respect to x. Find the function values at the critical number/s and at the endpoints. What is the largest possible volume of the box? What is the length of the side of the cut-out square that will make the box which has the largest possible volume?

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