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Now recall the Simple Power Rule where n # - 1 and C is the constant of integration. 1 + יX .+ C dx = n + 1 We note that we can write 8 x dx as 8 | x' dx. Therefore, n = and n + 1 = Applying the Simple Power Rule gives the following result. (Use C for the constant of integration.) 8 x dx =

Now recall the Simple Power Rule where n # - 1 and C is the constant of integration. 1 + יX .+ C dx = n + 1 We note that we can write 8 x dx as 8 | x' dx. Therefore, n = and n + 1 = Applying the Simple Power Rule gives the following result. (Use C for the constant of integration.) 8 x dx =

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Step 1 Recall the Constant Multiple Rule where k is a constant and f(x) is a function. kf(x) dx = k f(x) dx For 8x dx, we have k = 8| 8 and f(x) = x. Applying the Constant Multiple Rule gives the following result. 8x dx = 8 8 х dx Step 2 Now recall the Simple Power Rule where n + 1 and C is the constant of integration. x" dx = + 1 + C n + 1 We note that we can write 8 х ах as 8 x- dx. Therefore, n = and n + 1 = Applying the Simple Power Rule gives the following result. (Use C for the constant of integration.) 8 x dx = Submit Skip (you cannot come back).
Transcribed Image Text:Step 1 Recall the Constant Multiple Rule where k is a constant and f(x) is a function. kf(x) dx = k f(x) dx For 8x dx, we have k = 8| 8 and f(x) = x. Applying the Constant Multiple Rule gives the following result. 8x dx = 8 8 х dx Step 2 Now recall the Simple Power Rule where n + 1 and C is the constant of integration. x" dx = + 1 + C n + 1 We note that we can write 8 х ах as 8 x- dx. Therefore, n = and n + 1 = Applying the Simple Power Rule gives the following result. (Use C for the constant of integration.) 8 x dx = Submit Skip (you cannot come back).
Find the equation of the function f whose graph passes through the point. Derivative Point f(x) = 5Vx (25, 420) STEP 1: Begin by rewriting the derivative with exponents. f'(x) 5x STEP 2: Find the general solution: antiderivative of f'(x). (Use C for the constant of integration.) f(x) %D STEP 3: Substitute the initial conditions to solve for C. 25 420 + C = 420 С % STEP 4: Find the particular solution of the function. f(x) =
Transcribed Image Text:Find the equation of the function f whose graph passes through the point. Derivative Point f(x) = 5Vx (25, 420) STEP 1: Begin by rewriting the derivative with exponents. f'(x) 5x STEP 2: Find the general solution: antiderivative of f'(x). (Use C for the constant of integration.) f(x) %D STEP 3: Substitute the initial conditions to solve for C. 25 420 + C = 420 С % STEP 4: Find the particular solution of the function. f(x) =
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