Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2017 | June | Q#2
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Question
Given , find the value of
when x=8, writing your answer in the form
where a is a rational number.
Solution
We are given;
We are required to find .
Gradient (slope) of the curve is the derivative of equation of the curve. Hence gradient of curve with respect to
is:
Therefore;
Rule for differentiation is of is:
Rule for differentiation is of is:
Rule for differentiation is of is:
We need to find the gradient of the curve when x=8.
Gradient (slope) of the curve at the particular point is the derivative of equation of the curve at that articular point.
Gradient (slope) of the curve
at a particular point
can be found by substituting x- coordinates of that point in the expression for gradient of the curve;
We have already found that;
Substitute in derivative of the equation of the curve.
Since ;
If we need a rational number in the denominator of a fraction, we need to follow procedure of “denominator rationalization” as given below.
ü If the denominator is of the form then multiply both numerator and denominator by
.
ü If the denominator is of the form then multiply both numerator and denominator by
.
ü If the denominator is of the form then multiply both numerator and denominator by
.
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