(a) The derivative a function by the limit process is given by the formula f '(x) = S(x+Ax)=f(x) lim AX0 Find the derivative of the given function by the limit process. 4x 1 f(x) =- x – 1 (b) Find an equation of the line that is tangent to the graph of f and parallel to the given line. f(x) = x³, 3x – y + 1 = 0

(a) The derivative a function by the limit process is given by the formula f '(x) = S(x+Ax)=f(x) lim AX0 Find the derivative of the given function by the limit process. 4x 1 f(x) =- x – 1 (b) Find an equation of the line that is tangent to the graph of f and parallel to the given line. f(x) = x³, 3x – y + 1 = 0

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 54E

See similar textbooks

Similar questions

Lim as h approaches 0=[5e^x - 5e^(x+h)]/[3h]=
lim x-->3 f(x)=8 and lim x--->3 g(x)= -4 1) limx--->3 (3f(x)-5g(x)) 2) lim x---> G(x)^3 + 50 / ( 5f(x)^(2/3) )
a. Locate the critical points of ƒ.b. Use the First Derivative Test to locate the local maximum and minimum values.c. Identify the absolute maximum and minimum values of the functionon the given interval (when they exist). ƒ(x) = -x3 + 9x on ⌊-4, 3⌋
The total cost and the total revenue (in dollars) for the production and sale of x ski jackets are given by C(x)=28x+37,960 and R(x)=200x−0.1x2 for 0≤x≤2000. (A) Find the value of x where the graph of R(x) has a horizontal tangent line. (B) Find the profit function P(x). (C) Find the value of x where the graph of P(x) has a horizontal tangent line. (D) Graph C(x), R(x), and P(x) on the same coordinate system for 0≤x≤2000. Find the break-even points. Find the x-intercepts of the graph of P(x).
Consider a differentiable function f with domain R and derivativesf'(x)=-aebx(1+bx) and f"(x)=-abebx(2+bx) , with a and b nonzero real numbers.The function has only one critical point x=-1/b and a local maximum at x=-1/bUse the Second Derivative test to find the value(s) of a and b
limit of x to infinity Square root(x^2-2x+1)-x
f(x)=(-0.7x2+6.8x+4.2)e-x^2 Find the critical points, inflection points and intercepts (if any) limits as x --> +/- infinity
Finding the Derivative by the Limit Process In the given question/s, find the derivative of the function by the limit process.:- f (x) =x2 + x - 3
i.) The slope of a line passing through the point (a,b) not on f(x), and a tangent to f(x) = x² can be found by: a. finding the limit of f(x) at x = 1 b. solving the forula x² - 2xa + b = 0 c. finding the difference between f(a) and (b) d. none of the above answers are correct ii.)The derivative of f(x)=aˣ where a is a positive real number can never equal zero because f(x) is either always increasing or decreasing for its entire domain. a. True b. False
solve f´(2) if f(x) = x^3 – 6x^2 + 9x + 3 a). For which x is the function decreasing? Show using derivatives. b). Determine the coordinates of the extremes of the function using derivatives andc). show with derivatives whether they are maximum, minimum or terrace points. Show both with character table and second derivatives.d) Determine the largest and smallest value of the function in the interval 0 ≤ x ≤ 5 withderivatives.
2. f(x) = x^3 − 27x (a) Use the derivative of the function f(x) to find all critical points. (b) Draw and use a graph to classify each critical point of f(x) as a local minimum, local maximum, or neither.
11. given f(x)=x3-4x2+5x-2 a.) State the y-intercept b.) Use the first derivative test, find all critical values, state the intervals where f(x) is increasing and any local maximum or minimum values for x. Show all work. c.) Use the second derivative test, find all critical values, find the intervals where f(x) is concave up or concave down, and state the x-coordinate for the inflection point if it exists. Show all work. Thank you!!