The curve C has equation y = 2×2 – 12x + 16

The curve C has equation y = 2×2 – 12x + 16. Find the gradient of the curve at the point P (5, 6)

To find the gradient of the curve at the point P (5, 6), we need to find the derivative of y with respect to x and then evaluate it at x = 5.

Given y = 2x^2 – 12x + 16, we can find dy/dx by differentiating each term separately:

dy/dx = d/dx(2x^2) – d/dx(12x) + d/dx(16)

Using the power rule of differentiation, we have:

dy/dx = 4x – 12

Now, substitute x = 5 into the equation:

dy/dx = 4(5) – 12 = 20 – 12 = 8

Therefore, the gradient of the curve at the point P (5, 6) is 8.

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