Find an equation of the line that is tangent to the graph of f and parallel to the given line.
,
A)
B)
C)
D)
E) both B and D

Question

​Find an equation of the line that is tangent to the graph of f and parallel to the given line. ​
​  ,  ​
A) ​ 
B) ​ 
C) ​ 
D) ​ 
E) ​both B and D

Quizplus · Accepted Answer

First, we need to find the slope of the tangent line to the graph of f at the given point. We can do this by taking the derivative of f and evaluating it at x=4:
f'(x) = 2x-7
f'(4) = 2(4)-7 = 1

So the slope of the tangent line is 1.

Next, we need to find the equation of the given line, which has the form y=x-3. We can see that the slope of this line is also 1, so any line parallel to it will have the same slope.

Finally, we can use the point-slope form of a line to find the equation of the tangent line:
y-4 = 1(x-3)
y-4 = x-3
y = x+1

Comparing this to the options, we see that it matches both B and D, so the answer is E.

​Find an Equation of the Line That Is Tangent to the Graph

Find an Equation of the Line That Is Tangent to the Graph