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Let f(x) = 2x³ + x²-x+3 on the interval [-1.5, 5]. Use calculus and algebra to justify all answers. Round answers to 3 decimal places. i. Compute the first derivative. ii. Note that f is a polynomial and is thus continuous and differentiable for all real values of x. Use the derivative to find all critical points. iii. For which x-values is f(x) increasing? (Use intervals)

Let f(x) = 2x³ + x²-x+3 on the interval [-1.5, 5]. Use calculus and algebra to justify all answers. Round answers to 3 decimal places. i. Compute the first derivative. ii. Note that f is a polynomial and is thus continuous and differentiable for all real values of x. Use the derivative to find all critical points. iii. For which x-values is f(x) increasing? (Use intervals)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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(b) Let f(x) = 2x³ + x²-x+3 on the interval [-1.5, 5]. Use calculus and algebra to justify all answers. Round answers to 3 decimal places. i. Compute the first derivative. ii. Note that f is a polynomial and is thus continuous and differentiable for all real values of x. Use the derivative to find all critical points. iii. For which x-values is f(x) increasing? (Use intervals) iv. For which x-values is f(x) decreasing? v. Compute the second derivative. vi. For which x-values is f(x) concave up? vii. For which x-values is f(x) concave down? viii. Identify a critical point that gives a local maximum and explain how you know there is a maximum using the first derivative test. ix. Identify a critical point that gives a local minimum and explain how you know there is a minimum using the second derivative test. x. Classify each endpoint as either a local maximum or local minimum. xi. Check your work by graphing f(x).
Transcribed Image Text:(b) Let f(x) = 2x³ + x²-x+3 on the interval [-1.5, 5]. Use calculus and algebra to justify all answers. Round answers to 3 decimal places. i. Compute the first derivative. ii. Note that f is a polynomial and is thus continuous and differentiable for all real values of x. Use the derivative to find all critical points. iii. For which x-values is f(x) increasing? (Use intervals) iv. For which x-values is f(x) decreasing? v. Compute the second derivative. vi. For which x-values is f(x) concave up? vii. For which x-values is f(x) concave down? viii. Identify a critical point that gives a local maximum and explain how you know there is a maximum using the first derivative test. ix. Identify a critical point that gives a local minimum and explain how you know there is a minimum using the second derivative test. x. Classify each endpoint as either a local maximum or local minimum. xi. Check your work by graphing f(x).
Expert Solution
Step 1: Determine the given function.

The given polynomial function is f left parenthesis x right parenthesis equals 2 x cubed plus x squared minus x plus 3 on the interval left square bracket negative 1.5 comma 5 right square bracket.



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