Chapter 3: Q. 3 (page 136)

Find the average rate of change of $f (x) = 3 x^{2} - 2$ from 2 to 4.

Short Answer

Expert verified

The average rate of change is $\frac{∆ y}{∆ x} = 18 .$

Step by step solution

Step 1. Given Information

Given that $f (x) = 3 x^{2} - 2,$ and $x = 2$ to $x = 4 .$

Step 2. Solution

The average rate of change of function $f (x)$ from $x = x_{1}$ to $x = x_{2}$ is: -

$\frac{∆ y}{∆ x} = \frac{f (x_{2}) - f (x_{1})}{x_{2} - x_{1}} .$

Now, the average rate of function $f (x) = 3 x^{2} - 2$ from $x = 2$ to $x = 4$ is :-

$\frac{∆ y}{∆ x} = \frac{f (4) - f (2)}{4 - 2} \frac{∆ y}{∆ x} = \frac{(3 \times 4^{2} - 2) - (3 \times 2^{2} - 2)}{2} \frac{∆ y}{∆ x} = \frac{(48 - 2) - (12 - 2)}{2} \frac{∆ y}{∆ x} = \frac{36}{2} \frac{∆ y}{∆ x} = 18 .$

Step 3. Final Answer

Hence, $\frac{∆ y}{∆ x} = 18 .$

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Find the average rate of change of $f (x) = 3 x^{2} - 2$ from 2 to 4.

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Step by step solution

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Step 2. Solution

Step 3. Final Answer

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Find the average rate of change of $f (x) = 3 x^{2} - 2$ from 2 to 4.