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Block 1
Derivative Graphs
What is to be learned?
• How to sketch y = f/
(x) if given y = f(x)
y = f(x)
f/
(x) = 0
y = f/
(x)
m is
positive
f/
(x) above
axis
m is
negative
f/
(x) below
axis
m is
positive
f/
(x) above
axis
m is
negative
f/
(x) below
axis
y = f(x)
y = f/
(x)
+
above
-
below
above
below
+ -
y = f(x)
y = f/
(x)
+-
above
below
Sketching y = f/
(x)
• Draw directly below y = f(x)
• SVs on y = f(x) →
• +ve gradient on y = f(x) →
• -ve gradient on y = f(x) →
zero on y = f/
(x)
(on x axis)
above x axis
below x axis
y = f(x)
y = f/
(x)
-
below
above
below
+ -
(-3 , -2)
(2 , 1)
-3 2
y values
irrelevant
y = f(x)
y = f/
(x)
+
above
-
below
above
below
+ -
(-3 , 2)
(1 , -2)
(4 , 1)
-3 1 4
Key
Question
Copy y = f(x) and
sketch y = f/
(x)

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Derivative graphs

  • 2. What is to be learned? • How to sketch y = f/ (x) if given y = f(x)
  • 3. y = f(x) f/ (x) = 0 y = f/ (x) m is positive f/ (x) above axis m is negative f/ (x) below axis m is positive f/ (x) above axis m is negative f/ (x) below axis
  • 4. y = f(x) y = f/ (x) + above - below above below + -
  • 5. y = f(x) y = f/ (x) +- above below
  • 6. Sketching y = f/ (x) • Draw directly below y = f(x) • SVs on y = f(x) → • +ve gradient on y = f(x) → • -ve gradient on y = f(x) → zero on y = f/ (x) (on x axis) above x axis below x axis
  • 7. y = f(x) y = f/ (x) - below above below + - (-3 , -2) (2 , 1) -3 2 y values irrelevant
  • 8. y = f(x) y = f/ (x) + above - below above below + - (-3 , 2) (1 , -2) (4 , 1) -3 1 4 Key Question Copy y = f(x) and sketch y = f/ (x)