Average Gradient (Grade 11 NSC Matric Mathematics): Flashcards

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Average Gradient
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What does average gradient measure?

Overall rate of change between two points on a curve

Define secant line

Straight line passing through two points on a curve

Basic formula for average gradient

y2−y1x2−x1\frac{y_2 - y_1}{x_2 - x_1}

What is 'rise over run'?

Change in y divided by change in x (average gradient mnemonic)

Difference quotient formula

f(a+h)−f(a)h\frac{f(a+h) - f(a)}{h}

Secant line becomes what as points approach each other?

Tangent line

Define instantaneous gradient

Gradient at a point when two points coincide

What does negative average gradient indicate?

Function is decreasing

Average gradient for f(x)=x2f(x) = x^2 between aa and a+ha+h

2a+h2a + h

Average gradient between A(-3,7) and C(-1,-1)

−4-4

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