Gradient of a Curve (HSC SSCE Mathematics Advanced): Flashcards

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Gradient of a Curve
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Gradient formula for line through (x1,y1)(x_1,y_1) and (x2,y2)(x_2,y_2)

m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}

Definition of tangent to a curve

Straight line intersecting curve at exactly one point

Gradient of curve at a point equals

Gradient of tangent line at that point

Gradient when tangent is horizontal

Zero

Definition of secant line

Straight line through two distinct points on curve

Secant gradient for points P(c,f(c))P(c,f(c)) and Q(c+h,f(c+h))Q(c+h,f(c+h))

f(c+h)f(c)h\frac{f(c+h) - f(c)}{h}

What happens to secant as h0h \to 0

Secant approximates tangent; gradient approaches tangent gradient

What is the derivative of f(x)f(x)

The gradient function of f(x)f(x)

Alternative notations for derivative of f(x)f(x)

f(x)f'(x) or dydx\frac{dy}{dx} or yy'

What does f(a)f'(a) represent

Gradient of tangent to curve at x=ax = a

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