0
$\begingroup$

Find the average rate of change from $1$ to $x$ for the equation $2x^2 + x$. I tried the solving method but it did not help.

$\endgroup$
  • 1
    $\begingroup$ Can you actually show what you did so we can spot the issue you mention? Regards $\endgroup$ – Amzoti Sep 2 '13 at 1:55
1
$\begingroup$

Recall that the definition of the average rate of change of a function $f$ between $x = a$ and $x = b$ is defined to be

$$\frac{f(b) - f(a)}{b - a}$$

Now returning to your example, we have $f(x) = 2x^2 + x$, and $a = 1$, $b = x$. This leads to an average rate of change of

$$\frac{f(x) - f(1)}{x - 1} = \frac{(2x^2 + x) - (2 \cdot 1^2 + 1)}{x - 1} = \frac{2x^2 + x - 3}{x - 1}$$

Now we can simplify this slightly, by noting that

$$2x^2 + x - 3 = (x - 1)(2x + 3)$$

I'll leave the details to you.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.