The first graph is the solution for given table and the linear equation is y=3x+2.
<u>Step-by-step explanation:</u>
The linear equation of the line is y=mx+c.
where m is the slope and c is the y intercept.
The slope
Choose two points (0,2) and(1,5).
y=3x+c.
To find the y-intercept value substitute (0,2) in the equation.
2=0+c.
c=2.
∴y=3x+2.
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:
AnswerThe equation of the tangent line to f(x) and x = 3 is:
