Explanation
We must the tangent line at x = 3 of the function:
The tangent line is given by:
Where:
• m is the slope of the tangent line of f(x) at x = h,
,
• k = f(h) is the value of the function at x = h.
In this case, we have h = 3.
1) First, we compute the derivative of f(x):
2) By evaluating the result of f'(x) at x = h = 3, we get:
3) The value of k is:
4) Replacing the values of m, h and k in the general equation of the tangent line, we get:
Plotting the function f(x) and the tangent line we verify that our result is correct:
Answer
The equation of the tangent line to f(x) and x = 3 is:
Given the function :
![f(x)=\sqrt[]{x+2}+1](https://tex.z-dn.net/?f=f%28x%29%3D%5Csqrt%5B%5D%7Bx%2B2%7D%2B1)
We need to find each missing value
Given x = -3 , -2 , -1 , 2 , 7
So, substitute with each value of x to find the corresponding value of f(x)
![x=-3\rightarrow f(x)=\sqrt[]{-3+2}+1=\sqrt[]{-1}+1](https://tex.z-dn.net/?f=x%3D-3%5Crightarrow%20f%28x%29%3D%5Csqrt%5B%5D%7B-3%2B2%7D%2B1%3D%5Csqrt%5B%5D%7B-1%7D%2B1)
So, there is no value for f(x) at x = -3 (the function undefined because the square root of -1)
![\begin{gathered} x=-2\rightarrow f(x)=\sqrt[]{-2+2}+1=\sqrt[]{0}+1=0+1=1 \\ \\ x=-1\rightarrow f(x)=\sqrt[]{-1+2}+1=\sqrt[]{1}+1=1+1=2 \\ \\ x=2\rightarrow f(x)=\sqrt[]{2+2}+1=\sqrt[]{4}+1=2+1=3 \\ \\ x=7\rightarrow f(x)=\sqrt[]{7+2}+1=\sqrt[]{9}+1=3+1=4 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%3D-2%5Crightarrow%20f%28x%29%3D%5Csqrt%5B%5D%7B-2%2B2%7D%2B1%3D%5Csqrt%5B%5D%7B0%7D%2B1%3D0%2B1%3D1%20%5C%5C%20%20%5C%5C%20x%3D-1%5Crightarrow%20f%28x%29%3D%5Csqrt%5B%5D%7B-1%2B2%7D%2B1%3D%5Csqrt%5B%5D%7B1%7D%2B1%3D1%2B1%3D2%20%5C%5C%20%20%5C%5C%20x%3D2%5Crightarrow%20f%28x%29%3D%5Csqrt%5B%5D%7B2%2B2%7D%2B1%3D%5Csqrt%5B%5D%7B4%7D%2B1%3D2%2B1%3D3%20%5C%5C%20%20%5C%5C%20x%3D7%5Crightarrow%20f%28x%29%3D%5Csqrt%5B%5D%7B7%2B2%7D%2B1%3D%5Csqrt%5B%5D%7B9%7D%2B1%3D3%2B1%3D4%20%5Cend%7Bgathered%7D)
the graph of the function and the points will be as shown in the following image :
Answer: x=-3 y=7.
Step-by-step explanation:
Answer:
It will take 3.2 hours for 8 inches of snow to fall.
Step-by-step explanation:
You can solve this be going "backwards".
You have 2.5 inches of snow falling per hour for x hours until you get 8 inches of snow, which can be represented like this:
2.5x=8 From here you being to solve by isolating x on one side of the equation. You would divide both sides by 2.5 to do this
2.5x=8
/2.5 /2.5
8 divided by 2.5 is 3.2 and you then get
x=3.2
It takes 3.2 hours for 8 inches of snow to fall
