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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)

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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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).
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