Determine the equation of the tangent line to the graph of f(x) = -4x^2 + 11x - 2 at x = 2 that is parallel to the line y = 3x - 1.

Is that really what the problem says? If so, no wonder you are confused! That question, as stated, has

**no** answer.

You know that the derivative of a function, at a given point, is the slope of the tangent line. The line y= 3x- 1 has slope 3 so any line parallel to that also has slope 3. So you want to find a point on the curve that has derivative 3:

f'(x)= -8x+ 11. At "x= 2" as you wrote, f'(2)= -16+ 11= 5, NOT 3. The tangent line at x= 2 is NOT parallel to y= 3x- 1.

However, it the problem said only "Determine the equation of the tangent line to the graph of f(x) = -4x^2 + 11x - 2 that is parallel to the line y = 3x - 1"

**without** the "at x= 2" then it is quite doable. The slope of the tangent line is f'= -8x+ 11= 3 gives x= 1 (NOT 2). At x= 1 f(x)= -4+ 11- 2= 5 so the equation of the tangent line at x= 1 is y= 3(x- 1)+ 5= 3x+ 2.