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Calculus
The Gradient Of A Curve At A Point
How do we find the gradient at a given point on a curve?
[1] Find the general gradient of the curve using dy/dx
[2] Substitute the x coordinate value of the given point
into the expression found for dy/dx
Example:
Find the gradient of the curve
y = 2x2 + 3x + 4
at the point (2,5)
y = 2x2 + 3x + 4
dy/dx = 4x + 3
At the point (2,5) x = (2)
dy/dx = 4(2) + 3 = 8 + 3 = 11
The gradient of the curve at the point (2,5) is 11.
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