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Compute the instantaneous rate of change of the function at at x = a. f(x)=23-6x, a = -6 OA. -6 OB. -36 O C. 17 D. 36

Compute the instantaneous rate of change of the function at at x = a. f(x)=23-6x, a = -6 OA. -6 OB. -36 O C. 17 D. 36

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem Statement:** Compute the instantaneous rate of change of the function at \( x = a \). Given: \[ f(x) = 23 - 6x, \quad a = -6 \] **Options:** - A. \(-6\) - B. \(-36\) - C. \(17\) - D. \(36\) **Explanation:** The instantaneous rate of change of a function at a particular point is given by the derivative of the function evaluated at that point. For the function \( f(x) = 23 - 6x \), the derivative \( f'(x) \) is the coefficient of \( x \) in the expression, which is \(-6\). Thus, the instantaneous rate of change at \( x = a = -6 \) is \(-6\), matching option A.
Transcribed Image Text:**Problem Statement:** Compute the instantaneous rate of change of the function at \( x = a \). Given: \[ f(x) = 23 - 6x, \quad a = -6 \] **Options:** - A. \(-6\) - B. \(-36\) - C. \(17\) - D. \(36\) **Explanation:** The instantaneous rate of change of a function at a particular point is given by the derivative of the function evaluated at that point. For the function \( f(x) = 23 - 6x \), the derivative \( f'(x) \) is the coefficient of \( x \) in the expression, which is \(-6\). Thus, the instantaneous rate of change at \( x = a = -6 \) is \(-6\), matching option A.
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