Question

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

Answer 1

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)

point-gradient formula

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

Answer 2

`10`

Explanation:

`"the average rate of change is a measure of the slope of"`
`"the "color(blue)"secant line"" in the closed interval [a,b]"`

`•color(white)(x)(f(b)-f(a))/(b-a)`

`" here "a=4" and "b=6`

`f(b)=f(6)=38" and "f(a)=f(4)=18`

`rArr"average rate of change "=(38-18)/(6-4)=10`