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The demand function for a certain product is represented by the equation: where is the number of…
The demand function for a certain product is represented by the equation: $p = ax^2 + bx + c$ where $x$ is the number of units demanded and $p$ is the price per unit.
Answer the following questions by choosing the correct option:
(i)[2.0]
The revenue function $R(x)$ is:
- (a)$ax^3 + bx^2 + cx$
- (b)$ax + b + \frac{c}{x}$
- (c)$ax^3 + bx^2 + cx + d$
- (d)$2ax + b$
(ii)[2.0]
The marginal revenue $MR(x)$ is:
- (a)$a - \frac{c}{x^2}$
- (b)$3ax^2 + 2bx + c$
- (c)$3ax^3 + 2bx^2 + c$
- (d)$2a$
(iii)[2.0]
The slope of the marginal revenue is:
- (a)0
- (b)$6ax + 2b$
- (c)$\frac{2c}{x^3}$
- (d)$9ax^2 + 4bx$
(iv)[2.0]
Values of $x$, for which marginal revenue increases is:
- (a)$x > -\frac{b}{3a}$
- (b)$x < -\frac{b}{3a}$
- (c)$x = -\frac{b}{3a}$
- (d)$x \le -\frac{b}{3a}$
Answer
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From ISC 2022 Specimen Mathematics Paper 1, question 33.