# How do you find the average rate of change of f(x)=x^2+2 over [4,6]?

Mar 25, 2018

I assume u mean equation of the tangent at point (4,6).

If u mean rate of change for whole function, answer is just 2x.

#### Explanation:

I derive the function.

So when I derive f(x) I get 2x.

Subbing in my point I have 2(4) which is 8.

So 8 is my gradient and I have point (4,6)

y-6=8(x-4)
y-6=8x-4
8x-y+2=0

Mar 25, 2018

$10$

#### Explanation:

$\text{the average rate of change is a measure of the slope of}$
$\text{the "color(blue)"secant line"" in the closed interval [a,b]}$

•color(white)(x)(f(b)-f(a))/(b-a)

$\text{ here "a=4" and } b = 6$

$f \left(b\right) = f \left(6\right) = 38 \text{ and } f \left(a\right) = f \left(4\right) = 18$

$\Rightarrow \text{average rate of change } = \frac{38 - 18}{6 - 4} = 10$