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4. Suppose that f(x) = e²5e +. Find the domain and range of this function. Find all maxima and minima of this function. Plot the function. Hint: the function can be factored. 12.

4. Suppose that f(x) = e²5e +. Find the domain and range of this function. Find all maxima and minima of this function. Plot the function. Hint: the function can be factored. 12.

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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-2.25 4 4. Suppose that f(x) = e² - 5e +4. Find the domain and range of this function. Find all maxima and minima of this function. Plot the function. Hint: the function can be factored. 1 2 2 Rf = [A₁ ∞0) = [2.25,00) 2 The function can be written: f(x) = (ex-4) (e^-,) Df = R (all of the real line) en 2.5 A= min value of the first and fid we will it soon. 22 f(x) = 2e²²-5ex f²=0 => e²^² (2e²-5) = 0 The only solution is ex=2.5 Ana x = ln (2.5) 5 2x 20²* +2e²² -se", f" = 4e²z-5ex = > 0 So, there is a minimm at x= lu2.5 x.9163 Value of the first at x = ln 25. if (luz-5) = 2en1.5 = e f(x) has zero When C² = 4 = 1. = -Se = (2.5) ²-5 (2.5) +4 6.25 12.5 +4 -2.25 When ex=1 x=0 o whef co In 2.55 +4 Pt of inflection (x=lwa) +"=0 = €² (4e ²-5)=0 x = ln F/4. X-223 slope is the same · Sign 1... side of l
Transcribed Image Text:-2.25 4 4. Suppose that f(x) = e² - 5e +4. Find the domain and range of this function. Find all maxima and minima of this function. Plot the function. Hint: the function can be factored. 1 2 2 Rf = [A₁ ∞0) = [2.25,00) 2 The function can be written: f(x) = (ex-4) (e^-,) Df = R (all of the real line) en 2.5 A= min value of the first and fid we will it soon. 22 f(x) = 2e²²-5ex f²=0 => e²^² (2e²-5) = 0 The only solution is ex=2.5 Ana x = ln (2.5) 5 2x 20²* +2e²² -se", f" = 4e²z-5ex = > 0 So, there is a minimm at x= lu2.5 x.9163 Value of the first at x = ln 25. if (luz-5) = 2en1.5 = e f(x) has zero When C² = 4 = 1. = -Se = (2.5) ²-5 (2.5) +4 6.25 12.5 +4 -2.25 When ex=1 x=0 o whef co In 2.55 +4 Pt of inflection (x=lwa) +"=0 = €² (4e ²-5)=0 x = ln F/4. X-223 slope is the same · Sign 1... side of l
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