# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Feb-Mar | (P1-9709/12) | Q#7

Hits: 842

Question

The function f is defined for by .

i.       Find and .

The first, second and third terms of a geometric progression are respectively , and .

ii.       Find the value of the constant k.

Solution

i.

We are given the function;  Therefore; Rule for differentiation of is:  Therefore;  Second derivative is the derivative of the derivative. If we have derivative of the curve as , then  expression for the second derivative of the curve is;  Rule for differentiation of is:    ii.

We are given that the first, second and third terms of a geometric progression are respectively , and .

Let’s find first three terms of the Geometric Progression (G.P).                        Hence, first three terms of the Geometric Progression (G.P).   Expression for Common Ratio ( ) in a Geometric Progression (G.P) is;             