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Gradient

Gradient. A gradient describes the slope of a line. The gradient of a straight line is constant . But on a curve the gradient is different at different points on the curve. The G radient F unction. A gradient function describes the gradient of a graph.

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Gradient

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  1. Gradient A gradient describes the slope of a line. The gradient of a straight line is constant. But on a curve the gradient is different at different points on the curve.

  2. The Gradient Function A gradient function describes the gradient of a graph. If the graph is f(x) then the gradient function is f’(x). If the graph is y then the gradient function is

  3. Sketching Gradient Functions The rules: Where f(x) is sloping up then f’(x) is positive so it is above the x-axis Where f(x) is sloping down then f’(x) is negative so it is below the x-axis Where f(x) is has a turning point then f’(x) is 0 so it is on the x-axis Sloping down = negative gradient Sloping up = positive gradient Turning point = 0 gradient

  4. For example: So f’(x)must be: positive, 0, negative, 0, positive f(x) is going :up, t.p., down, t.p., up

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