Average Gradient (Grade 11 NSC Matric Mathematics): Quizzes

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Average Gradient
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What does the average gradient between two points on a curve measure?

The overall rate of change

What is the name of the straight line that passes through two points on a curve?

Secant line

Which formula calculates the average gradient between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2)?

y2−y1x2−x1\frac{y_2 - y_1}{x_2 - x_1}

What is the expression f(a+h)−f(a)h\frac{f(a+h) - f(a)}{h} called?

Difference quotient

What happens to the secant line as two points on a curve get closer together?

It approaches the tangent line

Find the average gradient between A(−3,7)A(-3, 7) and C(−1,−1)C(-1, -1).

−4-4

For g(x)=x2g(x) = x^2, what is the average gradient between (a,g(a))(a, g(a)) and (a+h,g(a+h))(a+h, g(a+h))?

2a+h2a + h

What does a negative average gradient indicate about a function?

The function is decreasing

As hh approaches 0, what does the average gradient approach?

The instantaneous gradient

For y=x2y = x^2, what is the instantaneous gradient at point (a,a2)(a, a^2)?

2a2a

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