1. For the relation wc + w3 = 3c+ 9, find an expression for dc/dw.2. (a) Suppose for a certain product, P = 30x – 0.6x? – 100, where P is total profit (in dollars) frommaking and selling x units. By differentiating this equation with respect to time t, derive an equationthat relates x, dx/dt and dP/dt.

Given:-the relation wc2+w3=3c+9To find: dcdwsolution:wc2+w3=3c+9differentiate both sides with…

Answered: 1. For the relation wc + w3 = 3c+ 9,…

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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Question

1. For the relation wc + w3 = 3c+ 9, find an expression for dc/dw.
2. (a) Suppose for a certain product, P = 30x – 0.6x? – 100, where P is total profit (in dollars) from
making and selling x units. By differentiating this equation with respect to time t, derive an equation
that relates x, dx/dt and dP/dt.

Expert Solution

Step 1

$G i v e n : - t h e r e l a t i o n w c^{2} + w^{3} = 3 c + 9 T o f i n d : \frac{d c}{d w} s o l u t i o n : w c^{2} + w^{3} = 3 c + 9 d i f f e r e n t i a t e b o t h s i d e s w i t h r e s p e c t t o w (w \frac{d}{d w} (c^{2}) + c^{2} \frac{d}{d w} (w)) + \frac{d}{d w} (w^{3}) = \frac{d}{d w} (3 c) + \frac{d}{d w} (9) (w (2 c) \frac{d c}{d w} + c^{2}) + 3 w^{2} = 3 \frac{d c}{d w} + 0 2 c w \frac{d c}{d w} + c^{2} + 3 w^{2} = 3 \frac{d c}{d w} (2 c w - 3) \frac{d c}{d w} = - c^{2} - 3 w^{2} \frac{d c}{d w} = \frac{- c^{2} - 3 w^{2}}{(2 c w - 3)} = \frac{c^{2} + 3 w^{2}}{3 - 2 c w} A n s$