Help me verify my answer

[Jacob]

Find the value of where the curve y = 2x^2 - 4x +1 has a gradient 4.
My working:
dy/dx = 2(2x) - 4 = 4x - 4
x = 4, dy/dx = 4(4) - 4 = 12#

But my lecturer answer is 2. I'm not sure where I went wrong.

 

[Otis]

Find the value of x where the … gradient [equals] 4 …

Hello. I added the x shown in green above.

You found the correct formula for the gradient (dy/dx) at any x:

dy/dx = 4x - 4

They want to know where the gradient equals 4, so substitute 4 for dy/dx.

4 = 4x - 4

Solve, to find x = 2

… x = 4, dy/dx = 4(4) - 4 = 12 …

What you had done was to calculate the gradient at x=4.

The gradient is 12, when x equals 4.

The gradient is 4, when x equals 2.

?

 

[Steven G]

As Otis pointed out, the gradient is dy/dx, NOT x! So if the gradient is 4, then substitute 4 for dy/dx