Find an equation of the line tangent to at x = 2.
A) y = -2x + 3
B) y = -2x
C) y = 2x + 3
D) y = -2x + 5

Question

Find an equation of the line tangent to  at x = 2.
A) y = -2x + 3 
B) y = -2x 
C) y = 2x + 3 
D) y = -2x + 5

Quizplus · Accepted Answer

To find the equation of the tangent line, we need to find the slope of the tangent line.

To do that, we need to take the derivative of the function at x=2:

f'(x) = -4x + 2

f'(2) = -8 + 2 = -6

So the slope of the tangent line at x=2 is -6.

Now we use the point-slope form of a line, with the point (2,3) on the line and the slope of -6:

y - 3 = -6(x - 2)

y = -6x + 15

Simplifying this equation, we get:

y = -2x + 5

So the equation of the tangent line is y = -2x + 5, which is choice (D).

Find an Equation of the Line Tangent to at X