Comparing Functions In Exercises 69-74, use L’'Hopital’'s Rule to determine the comparative rates of increase of the functions
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- Part 1: A derivative computation using the chain rule Suppose F(x) is any function that is differentiable for all real numbers x. Evaluate the following derivative. d -(F(x*)) = x^4+4x^3 dx Enter the derivative of F(x) as F'(x) using prime notation. Your answer should be in terms of F' and other functions of the variable x. Part 2: A derivative computation using the FTC Part 3: A composition of two functions Part 4: A derivative computation using the FTC and the chain rulearrow_forward(Differentiable Functions: Standard Analysis & Graph Sketching). Consider the function f(x) = −(2x+11x+16)/e^x(i) Make the standard analysis of the function f(x), that is: (1) make the combined sign chart of f' and f''; (ii) Use (i) to sketch the graph of f ;arrow_forwardMymathlab homeowork for business calculus: use the definition of the derivative, lim h-->0 (f+h)-f(x)/h, to find the following: f'(x) if f(x) = -2x+7. f(x)=?arrow_forward
- Poblem #3: Let f(x) = x'e-8x (a) On which interval is f increasing? (b) Which x-value(s) correspond to local maxima of f? (A) (0, ) (B)(-2, 0) (C)(-x, ) (D) (, c) (E)(0, ) Problem =3(a): Select v Part (a) choices. (A) 0 and (B) 0 (C) 3 Problem =3(b): Select v T Part (b) choices.arrow_forwardConsider the function g given by g(x) = |x - 2| +5. (a) For what x-value(s) is the function not differentiable? (b) Evaluate g'(0), g'(1), g'(5), and g'(10). (a) The function is not differentiable at x =. Textbook Ask my instructorarrow_forwardGraph of f(x) = LxJarrow_forward
- Identify f(x), g(x), and h(x) such that F(x) = f(g(h(x))) for the function F(x) VIn(x+ + 6) Answer O f(x) = x* + 6, g(x) 2 h(x) = Inx' 2 ofx) = x* + 6, g(x) = Inx, h(x) O f(x) = V, 8(x) : h(x) = x* + 6 Inx' of(x) = 2 g(x) = Inx, h(x) = x4 + 6arrow_forwardf(x) = ln(x2 + 6) What are the inflection points f(x) = x3 e−x On what intervals is the graph increasing and decreasingarrow_forwardFind the linearization of the function f(x)=(1/3x+2) at x=−1. L(x)= x The exact value f(x) The appoximate value L(x) -1.1 -1.01 -1.001arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage