a. Is f(x) continuous on the interval [-2,6]? b. Find and fully factor f'(x) = If so, it will have an absolute maximum and minimum. C. Are there any x values where the derivative does not exist? If so, list them: d. Set f'(x) = 0 and find the x values that satisfy the equation f'(x) = 0 and fall into the interval of interest. e. Draw a number line and label the endpoints and critical numbers. Above the number line, write in 0 or DNE where you know the value of the derivative. In between the points you labeled, write down the sign of the derivative, + or -. Use the factored form of f'(x) to figure out the signs the most easily. f. Based on the signs of the derivative, label the critical numbers as local maximum, local minimum, or neither. g. Calculate f"(x) = h. Where is f"(x) equal to 0, if ever? i. Draw another number line below for f"(x), show where f"(x) is positive and where it is negative, and label the intervals where f (x) is concave up or down.

a. Is f(x) continuous on the interval [-2,6]? b. Find and fully factor f'(x) = If so, it will have an absolute maximum and minimum. C. Are there any x values where the derivative does not exist? If so, list them: d. Set f'(x) = 0 and find the x values that satisfy the equation f'(x) = 0 and fall into the interval of interest. e. Draw a number line and label the endpoints and critical numbers. Above the number line, write in 0 or DNE where you know the value of the derivative. In between the points you labeled, write down the sign of the derivative, + or -. Use the factored form of f'(x) to figure out the signs the most easily. f. Based on the signs of the derivative, label the critical numbers as local maximum, local minimum, or neither. g. Calculate f"(x) = h. Where is f"(x) equal to 0, if ever? i. Draw another number line below for f"(x), show where f"(x) is positive and where it is negative, and label the intervals where f (x) is concave up or down.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter1: Functions

Section1.2: Functions Given By Tables

Problem 32SBE: Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it...

See similar textbooks

Similar questions

Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it continues on its course indefinitely. Let D(t) denote its distance from Earth after t years of travel. Do you expect that D has a limiting value?
bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
When a certain drug is taken orally, the concentration of the drug in the patient's bloodstream After t minutes is given by C(t)=0.06t0.0002t2 where 0t240 and concentration is measured in mg/L .When is the maximum serum concentration reached, and what is that maximum concentration?
Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval -,x1 and decreases on the interval x1,, then fx1 is a local minimum value.