Chapter 14: Q. 49 (page 883)

find the limit as x approaches c of the average rate of change of each function from c to x.
$c = 0; f (x) = 3 x^{3} - 2 x^{2} + 4$

Short Answer

Expert verified

The limit is $0$

Step by step solution

Step 1. Given information is

$c = 0; f (x) = 3 x^{3} - 2 x^{2} + 4$

Step 2. An average rate change of function f from point c to x

$\frac{∆ y}{∆ x} = \frac{f (x) - f (c)}{x - c} \frac{∆ y}{∆ x} = \frac{3 x^{3} - 2 x^{2} + 4 - (3 c^{3} - 2 c^{2} + 4)}{x - c} \frac{∆ y}{∆ x} = \frac{3 x^{3} - 2 x^{2} + 4 - (3 {(0)}^{3} - 2 {(0)}^{2} + 4)}{x - 0} \frac{∆ y}{∆ x} = \frac{3 x^{3} - 2 x^{2} + 4 - 4}{x} \frac{∆ y}{∆ x} = \frac{3 x^{3} - 2 x^{2}}{x} \frac{∆ y}{∆ x} = \frac{x (3 x^{2} - 2 x)}{x} \frac{∆ y}{∆ x} = 3 x^{2} - 2 x$

Step 3. Solving for limit we get,

$\lim_{x \to c} \frac{∆ y}{∆ x} = \lim_{x \to c} \frac{f (x) - f (c)}{x - c} \lim_{x \to c} \frac{∆ y}{∆ x} = \lim_{x \to c} (3 x^{2} - 2 x) \lim_{x \to c} \frac{∆ y}{∆ x} = 3 {(0)}^{2} - 2 (0) \lim_{x \to c} \frac{∆ y}{∆ x} = 0$

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find the limit as x approaches c of the average rate of change of each function from c to x.
$c = 0; f (x) = 3 x^{3} - 2 x^{2} + 4$

Short Answer

Step by step solution

Step 1. Given information is

Step 2. An average rate change of function f from point c to x

Step 3. Solving for limit we get,

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find the limit as x approaches c of the average rate of change of each function from c to x.c=0;f(x)=3x3-2x2+4

Short Answer

Step by step solution

Step 1. Given information is

Step 2. An average rate change of function f from point c to x

Step 3. Solving for limit we get,

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Mechanics Maths

Statistics

Decision Maths

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

find the limit as x approaches c of the average rate of change of each function from c to x.
$c = 0; f (x) = 3 x^{3} - 2 x^{2} + 4$