Chapter 2: Q. 8 (page 126)

For the function $f (x) = 3 x^{2} - 2 x + 4$ , find the average rate
of change of f from $3$ to $4$ .

Short Answer

Expert verified

The average rate of change of $f (x) = 3 x^{2} - 2 x + 4$ form $3$ to $4$ is $19$

Step by step solution

Step 1. Given data

The given function is

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

Step 2. The average rate of change

The average rate of change function is

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

Step 3. substitute values

substitute $3$ for aand $4$ for bin the average rate of change of function

$\frac{∆ y}{∆ x} = 3 (a + b) - 2 \frac{∆ y}{∆ x} = 3 (3 + 4) - 2 \frac{∆ y}{∆ x} = 3 (7) - 2 \frac{∆ y}{∆ x} = 21 - 2 \frac{∆ y}{∆ x} = 19$

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For the function $f (x) = 3 x^{2} - 2 x + 4$ , find the average rate
of change of f from $3$ to $4$ .

Short Answer

Step by step solution

Step 1. Given data

Step 2. The average rate of change

Step 3. substitute values

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For the function f(x)=3x2-2x+4, find the average rateof change of f from 3to 4.

Short Answer

Step by step solution

Step 1. Given data

Step 2. The average rate of change

Step 3. substitute values

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Pure Maths

Statistics

Decision Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

For the function $f (x) = 3 x^{2} - 2 x + 4$ , find the average rate
of change of f from $3$ to $4$ .