10 Find the critical point and the interval on which the given function is increasing or decreasing, and apply the First Derivative Test to the critical point. Letf(x)=x-4 ln(10x),x>0Critical Point =Isf a maximum or minumum at the critical point? ?The interval on the left of the critical point isOn this interval, fis ?✓while f' is ?The interval on the right of the critical point isOn this interval, fis ?whileis ?

Answered: Find the critical point and the…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Consider the function f(x)=ln (1+x2). a. Find all the critical values of f(x)=ln (1+x2). Using the first derivative test, identify the intervals of increase and intervals of decrease
Consider the function f(x,y)=2xy-1/2(x^4-y^4)+1 (a) Find all critical points of f(x,y). Once finding them, give the function value at each critical point. (b) Classify all of the critical points using the 2nd Derivative Test.
True of False: Derivative of (arctan(e^(-x^2))) = [-2xe^(-x^2)] / [1 + e^(-2x^2)] Show your solution
Leth(x) = arctan(x2+ 2x). Find all critical values (if any) ofhand use the second derivative test todetermine where all the local extrema of the function are. You should show all your work calculatingthe second derivative.
find the critical numbers of (if any), (b)find the open interval(s) on which the function is increasing ordecreasing, (c) apply the First Derivative Test to identify allrelative extrema
Let y = 2 ln x - 1/2x then the first derivative is....., the first order condition is..... and the value of x satisfying the FOC is...
Suppose that antibiotics are injected into a patient to treat a sinus infection. The antibiotics circulate in the blood, slowly diffusing into the sinus cavity while simultaneously being filtered out of the blood by the liver. The following is a model for the concentration (in µg/mL) of the antibiotic in the sinus cavity as a function of time (in hours) since the injection. C(t) = (e−αt − e −βt )/(β − α) , where α and β are constants with β > α > 0. (a) Using the first derivative test, find when the maximum concentration occurs. (Your argument must use the first derivative test.) (b) When does the rate of change of concentration begin to increase? (Your answer should be supported by a rigorous argument.)
Find an absolute minimum and absolute maximum,find a local minimum and local maximum, find the second derivative, and find the point of inflection show all work y= x-sinx, 0 less than or equal to x less than or equal to 2pie
Find first and second derivative, critical points, concavity, x and y intercepts, vert and horz asymptotes, dec/inc, and points of inflection for f(x) = ln(x)/x
Use Richardson extrapolation to find an improved estimate for the first derivative of y = cos x at x =π/4 using step sizes of h1 = π/3 and h2 = π/6. Employ centered differences of O(h2) for the initial estimates. Discuss from your results the effect of using Richardson extrapolation on the error of using centered differences.
take the derivative of this function - find the critical points in order to find the maximum and minimum values for your function - prove that the critical points represent maximum or minimum points (eg: with an interval table) - find the extreme points on your function Using this info Problem: An open-top cylindrical tank with a volume of 2000 cubic meters is to be constructed using steel. The steel used for the top and bottom costs 0.5 dollars per square meter, while the steel used for the sides costs 0.3 dollars per square meter. Determine the dimensions of the tank that will minimize the cost of steel used. arrow_forward Step 3: State the variables of the problem Variables: r: radius of the base of the cylinder in meters h: height of the cylinder in meters Function: The surface area of the cylindrical tank is given by: A = 2πrh + 2πr2 The cost of steel is given by: C = 0.5(2πr 2) + 0.3(2πrh) Objective: Minimize the cost of steel C. Domain: r and h must be positive…
give a problem and solution for differentiation rule of exponential and logarithmic functions in partial differentiation of function of U with respect to 3 independent variables x, y and z and solve ???z

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