2. gradient of a chord & first derivative
TRANSCRIPT
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8/18/2019 2. Gradient of a Chord & First Derivative
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GRADIENT OF A CHORD
0
P
Q
y = f(x)
y
x
Gradient of chord PQ =
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0
P
y = f(x)
y
x
GRADIENT OF THE TANGENT TO THE CURVE AND THE FIRT DERIVATIVE OF A FUNCTION
As the point Q moves nearer and
nearer to the point P such as ….as
shown in the diagram, the chord
PQ can be seen getting nearer andnearer to the tangent at point P.
= gradient of tangent to thecurve at point P
Therefore
,
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0
P
y = f(x)
y
x
Then, gradient chord P !
As point approaches point P, , therefore
sma"" change in y
sma"" change in x
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= gradient of tangent to
the curve at point P
#n ca"cu"us , we denote as
$ence represent s the gradient of tangent at a point P on
the curve
is a"so %nown as the first derivative of the function