The gradient of the curve y=2x^2-x+6 at the point (2,16)
At x = 2, y = 2(2)^2 - 2 + 6 = 2*4 + 4 = * + 4 = 12
The point (2,12) is a point on the curve y = 2x^2 - x + 6. The point (2,16) is not a point on this curve.
There is an error in the presentatiopn of the question (a typo)
We can show that the point (2.5,16) is a point on the curve y = 2x^2 - x + 6. (the origlnal curve)
And, the point (2,16) is a point on the curve y = 2x^2 + x + 6. (note change of sign for the x-component)
So, either the coordinates are wrong, or the curve is wrong.
Getting the sign wrong is a frequent error, so I'm going to assume that's what's happened here.
Let the question be: The gradient of the curve y = 2x^2 + x + 6 at the point (2,16)
The point (2, 16) is a pont on the given curve.
The gradient of a curve, y = f(x), is given by dy/dx.
For the given curve, dy/dx = 4x + 1
At x = 2, dy/dx = 4*2 + 1 = 8 + 1 = 9
Answer: At the point (2, 16) the slope of the curve is 9