Question

Let f(x) = -2 / (2x + 8). If h ? 0, then the difference quotient can be simplified as f(x + h) - f(x) / h = A / ((Bx + Ch + 8)(Dx + 8)), where A, B, C, and D are constants. (Note: It's possible for one or more of these constants to be 0.) Find the constants. A = , B = , C = , and D = . Use your answer from above to find f'(x) = lim h?0 f(x + h) - f(x) / h = . Finally, find each of the following: f'(1) = , f'(2) = , and f'(3) = .

Name: Let f(x) = -2 / (2x + 8). If h ? 0, then the difference quotient can be simplified as f(x + h) - f(x) / h = A / ((Bx + Ch + 8)(Dx + 8)), where A, B, C, and D are constants. (Note: It's possible for one or more of these constants to be 0.) Find the constants. A = , B = , C = , and D = . Use your answer from above to find f'(x) = lim h?0 f(x + h) - f(x) / h = . Finally, find each of the following: f'(1) = , f'(2) = , and f'(3) = .
Uploaded: 2022-10-29T19:09:52-08:00
Duration: 6 min 47 s
Channel: Avinash Vishwakarma

          Let f(x) = -2 / (2x + 8). If h ? 0, then the difference quotient can be simplified as f(x + h) - f(x) / h = A / ((Bx + Ch + 8)(Dx + 8)), where A, B, C, and D are constants. (Note: It's possible for one or more of these constants to be 0.) Find the constants. A = , B = , C = , and D = . Use your answer from above to find f'(x) = lim h?0 f(x + h) - f(x) / h = . Finally, find each of the following: f'(1) = , f'(2) = , and f'(3) = .

Let f(x) = -2 / (2x + 8). If h ? 0, then the difference quotient can be simplified as f(x + h) - f(x) / h = A / ((Bx + Ch + 8)(Dx + 8)), where A, B, C, and D are constants. (Note: It's possible for one or more of these constants to be 0.) Find the constants. A = , B = , C = , and D = . Use your answer from above to find f'(x) = lim h?0 f(x + h) - f(x) / h = . Finally, find each of the following: f'(1) = , f'(2) = , and f'(3) = .

Added by Erik N.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Avinash Vishwakarma

10/29/2022

Step 1

Step 1: Find the constants A and D: From the given difference quotient, we have: \[f(x + h) - f(x) = \frac{2x + 8}{(2x + 2h + 8)(2x + 8)}\] Comparing this with the simplified form (2x + 8) / (f(x)(Bx + Ch + 8)(Dx + 8)), we can see that A = 4 and D = 2. Show more…

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Let f(x). If h ≠ 0, then the difference quotient can be simplified as f(x+h) - f(x) / h = A / ((Bx + Ch + 8)(Dx + 8)), where A, B, C, and D are constants. (Note: It's possible for one or more of these constants to be 0.) Find the constants. Use your answer from above to find f'(x) = lim h→0 f(x + h) - f(x) / h. Finally, find each of the following: f'(1) = f'(2) = f'(3) =