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Consider the function: y = x¹ − 2x³+4x² +1. Find the x-coordinates of any maxima, minima and points of inflection and find the asymp- totic behaviour. Find where it is concave up or concave down. Give all your reasoning. Using this information, sketch this function.

Consider the function: y = x¹ − 2x³+4x² +1. Find the x-coordinates of any maxima, minima and points of inflection and find the asymp- totic behaviour. Find where it is concave up or concave down. Give all your reasoning. Using this information, sketch this function.

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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Consider the function:

 

a) b) c) Consider the function: 2x³+4x²+1. Find the x-coordinates of any maxima, minima and points of inflection and find the asymp- totic behaviour. Find where it is concave up or concave down. Give all your reasoning. Using this information, sketch this function. Consider the curve given by the parametric equations x = a cos³ 0, y = a sin³ 0, where a is a constant and is the parameter. Find the (x, y) coordinates on this curve where the tangent line to the curve is (a) horizontal and (b) vertical. Show that, for x, y real numbers, cos(x + iy) = cos 2 cosh y — i sin r sinh y . Using this result and the Cauchy-Riemann conditions, or otherwise, determine whether cos z is differentiable (i.e., analytic).
Transcribed Image Text:a) b) c) Consider the function: 2x³+4x²+1. Find the x-coordinates of any maxima, minima and points of inflection and find the asymp- totic behaviour. Find where it is concave up or concave down. Give all your reasoning. Using this information, sketch this function. Consider the curve given by the parametric equations x = a cos³ 0, y = a sin³ 0, where a is a constant and is the parameter. Find the (x, y) coordinates on this curve where the tangent line to the curve is (a) horizontal and (b) vertical. Show that, for x, y real numbers, cos(x + iy) = cos 2 cosh y — i sin r sinh y . Using this result and the Cauchy-Riemann conditions, or otherwise, determine whether cos z is differentiable (i.e., analytic).
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