Find an equation of the line that is tangent to the graph of the function and parallel to the line .

Question

Find an equation of the line that is tangent to the graph of the function  and parallel to the line  .

Quizplus · Accepted Answer

First, we need to find the derivative of the function 11eaa595_6689_d326_a696_73659d008b95_TB4584_11_TB4584_11:

f'(x) = 2x + 1

Since we want a line that is tangent to the graph of the function and parallel to the line 11eaa595_6689_fa37_a696_4d473c949007_TB4584_11_TB4584_11, we know that the slope of the tangent line must be equal to the slope of the given line.

The slope of the given line is 2, so the slope of the tangent line must also be 2. Now we can use the point-slope form of a line to find the equation of the tangent line.

We know that the tangent line passes through the point (2,8) (which is also on the graph of the function), so we have:

y - 8 = 2(x - 2)

Simplifying this equation, we get:

y = 2x + 4

Therefore, the correct answer is D.

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