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(i) Find the critical points of the function f(x) = x³ + x²-2x+1 and characterize them. Sketch a graph of the function. Find also the absolute minimum in the domain -2 ≤ x ≤ 1.

(i) Find the critical points of the function f(x) = x³ + x²-2x+1 and characterize them. Sketch a graph of the function. Find also the absolute minimum in the domain -2 ≤ x ≤ 1.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(i) Find the critical points of the function f(x) = x³ + x² - 2x+1 and characterize them. Sketch a graph of the function. Find also the absolute minimum in the domain -2 ≤ x ≤ 1. (ii) Make a contour plot of the function z(x, y) = -xy in the xy-plane, by drawing a collection of curves z(x, y) = c for different (positive and negative) values of the constant c. Try and sketch a graph of the function in the space of xyz coordinates (as a check you may want to compare that sketch with a computer/Python graph).
Transcribed Image Text:(i) Find the critical points of the function f(x) = x³ + x² - 2x+1 and characterize them. Sketch a graph of the function. Find also the absolute minimum in the domain -2 ≤ x ≤ 1. (ii) Make a contour plot of the function z(x, y) = -xy in the xy-plane, by drawing a collection of curves z(x, y) = c for different (positive and negative) values of the constant c. Try and sketch a graph of the function in the space of xyz coordinates (as a check you may want to compare that sketch with a computer/Python graph).
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