Inverse Function and Area
(a) Let
(b) Use the formula in part (a) to find the integral
(c) Use the formula in part (a) to find the area under the graph of
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Calculus: Early Transcendental Functions
- The weekly cost C, in dollars, of manufacturing x lightbulbs is C(x) = 7500+ V125x (a) Find the average rate of change of the weekly cost C of manufacturing from 100 to 150 lightbulbs. Give answer correct to two decimal places. Give proper units. (b) Find the instantaneous rate of change in the weekly cost when 125 lightbulbs are manufactured. Give answer correct to two decimal places. Give proper units.arrow_forward= -x³ + 3x² 3x and f(2) = -2. If g is the The function f is defined by f (x) = inverse function of f, what is the value of g' (-2)? %3D 3Darrow_forwardT fect 12 foet As depicted above, oil is leaking out of the cone into a cylinder (storage container) whose circular base has an area of 400m. The depth of the oil in the cone is changing at a rate of y-12 ft/min. (a) Create an expression for the volume of oil in the cone as a function of y. (b) At y-3, find the rate at whích the volume of oil in the cone is changing. Include units and a brief sentence in context. (c) Let h be the depth of the oil in the tank at the cylindrical storage container. Determine the rate that h is changing at the instant y-3. Include units and a brief sentence in context.arrow_forward
- F(x)= 7/(x+9) find the inversearrow_forwardFind the inverse function of f. f(x) = V x2 - 9, x2 3 STEP 1: Replace f(x) with y. Vx² - 9 STEP 2: Interchange x and y. X = STEP 3: Square each side. x2 = STEP 4: Add 9 to each side. y? STEP 5: Take square root of each side. = y STEP 6: Find the inverse function of f. (x) = x 2 0arrow_forward2x + 4 Let f be the one-to-one function given below. f(¤) - 5x + 6 (a) Find the inverse function of f (1.e., f (x).) f '(@) =| (b) Compute f 1(2). f '(2)=arrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage