Given the function f (x) = x'eX %3D 1. Show that f'(x) = -e*(x – 4)x and f"(x) = e¯*x²(x² – 8x + 12). 2. Find the domain of the function and its intercepts, if any. %3D 3. Construct a table summarizing the needed information about the graph of the function, such as the interval where the function is increasing/decreasing and concave upward/downward, local maximum and minimum and points of inflection, if any. 4. Sketch the graph of the function indicating any local extrema and points of inflection.

Given the function f (x) = x'eX %3D 1. Show that f'(x) = -e(x – 4)x and f"(x) = e¯x²(x² – 8x + 12). 2. Find the domain of the function and its intercepts, if any. %3D 3. Construct a table summarizing the needed information about the graph of the function, such as the interval where the function is increasing/decreasing and concave upward/downward, local maximum and minimum and points of inflection, if any. 4. Sketch the graph of the function indicating any local extrema and points of inflection.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.1: Tables And Trends

Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...

See similar textbooks

Similar questions

If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per second. What is the terminal velocity, and how long does it take the filter to reach 99 of terminal velocity? Use a table increment of 0.1 and given your answer to the nearest tenth of a second.
1.) Find the area under the curve y = x3 + 3x2 and the axis between x = 1 and x = 3. 2.) Evaluate the first derivative of the implicit function: 4x2 + 2xy + y2 = 0
Show mathematically that MRS is increasing for U=1-ex +e2y and is diminishing for U=lnX +LnY
Find the equation of the tangent line to the graph ofy = f(x) at x = x0 f(x) = ln x; x0 = e−1
Find the general solution using reduction of order. 1. y''=ln(x)
Suppose that a company’s marginal revenue from the manufacture and sale of eggbeaters is dr/ dx = 2 - 2/(x + 1)2, where r is measured in thousands of dollars and x in thousands of units. How much money should the company expect from a pro-duction run of x = 3 thousand eggbeaters? To find out, integrate the marginal revenue from x = 0 to x = 3.
Find the nth derivative of the function y=xlnx at x=1.
Find the linearization of the function k(x) = ln(x) when x= 1 and use it to estimate ln(1.1).
Find the differential dy of the given function y=extanx
Find the antiderivative of the function f(x)=3x-cos x-ln x
Find the linearizationsof the following functions at x = 0. ln (1 + x)
Use Richardson extrapolation to estimate the first derivative of y = cos x at x = π/ 4 using step sizesof h1 = π/ 3 and h2 = π/ 6. Employ centered differences of O(h2) for the initial estimates.