Consider the function # f(x)=1/sqrt(x+2)# on the interval [-1, 23], how do you find the average or mean slope of the function on this interval?

Question

Elijah Abram · Accepted Answer

The mean slope is #=-1/30#

The mean slope of a function #f(x)# over an interval #[a,b]# is

#=(f(b)-f(a))/(b-a)#

Here,

#f(x)=1/sqrt(x+2)#

#f(-1)=1/sqrt(-1+2)=1#

#f(23)=1/sqrt(23+2)=1/5#

Therefore,

the mean slope is

#=(f(23)-f(-1))/(23-(-1))#

#=(1/5-1)/(24)#

#=-4/5*1/24=-1/30#

Adam Adkins · Answer

undefined To find the average or mean slope of the function $ f(x) = \frac{1}{\sqrt{x+2}} $ on the interval $[-1, 23]$, you need to calculate the slope of the function at each point within the interval and then find the average of these slopes.

The slope of a function at a point can be found using the derivative of the function. In this case, you would need to find the derivative of $ f(x) $, which is $ f'(x) = -\frac{1}{2(x+2)^\frac{3}{2}} $.

Then, you evaluate the derivative at each point within the interval $[-1, 23]$ and calculate the slope at that point. After finding the slopes at all points, you sum them up and divide by the total number of points to get the average slope.

So, the average slope of the function on the interval $[-1, 23]$ is the sum of all individual slopes divided by the number of points in the interval.