# 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;  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 .    