Use the formula for instantaneous rate of change, approximating the limit by using smaller and smaller values of hh , to find the instantaneous rate of change for each function at the given value. f(x)=x^{x} at x=2

Step-by-step explanation:

Given

at

Required

The instantaneous rate of change

We have:

The instantaneous rate of change is:

implies that:

So, we have:

Keep reducing h but set a constant at 2

Notice that:

for and

Hence, the instantaneous rate of change is:

---- approximated

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is

hi! i think the answer is 1/2 : )