Average Gradient on a Curve (Grade 11) — Worksheet & Memo

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Grade 11 · Functions and Graphs

Average Gradient on a Curve (Grade 11)

WORKSHEET

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Date:

Mark

/ 25

Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

1
Determine the average gradient of f(x) = x² between x = 2 and x = 5.
(2)
2
Determine the average gradient of f(x) = x² + 1 between x = −1 and x = 2.
(2)
3
Write down the formula for the average gradient of f between x = a and x = b.
(2)
4
For f(x) = x², calculate the average gradient between x = 2 and x = 2,1 (to two decimal places).
(3)
5
Using the answer above, estimate the gradient of y = x² AT the point where x = 2.
(2)
6
Explain why the gradient of a curve cannot be given as a single number, but the gradient of a straight line can.
(3)
7
The average gradient of f between x = 0 and x = 4 is 0. Does this mean the graph is a horizontal line? Explain.
(3)
8
A ball's height is h(t) = 30t − 5t² metres. Determine its average velocity between t = 1 and t = 4 seconds.
(3)
9
What does the chord between two points on a curve become as the two points slide together?
(2)
10
For f(x) = 2x², determine the average gradient between x = 1 and x = 1 + h, and simplify your answer.
(3)

TOTAL: 25 marks