#### Mathematics

- Determine f`(x) from first principles if f(x) = 3x2
- On 1 June 2016 a bank granted Thabiso a loan of R250 000 at an interest rate of 15% p.a. compounded monthly, to buy a car. Thabiso agreed to repay the loan in monthly installments commencing on 1 July 2016 and ending 4 years later on 1 June 2020. However Thabiso was unable to make the first two installments and only commenced with the monthly installments on 1 September 2016.
- Given: f(x) = -x + 3 and g(x) = log2x
- Sketched below is the parabola f, with equation f(x) = -x2 + 4x -3 and a hyperbola g. with the equation (x-p)(y + t) = 3. B, the turning point of f, lies at the point of intersection of the asymptotes of g. A(-1;0) is the x-intercept of g.
- Sketched below is the graph of h(x) = ax, a > 0. R is the y-asymptote of h. The points P(2;9) and Q(b; 1⁄81) lie on h.
- The first four terms of a quadratic number pattern are -1; x; 3; x + 8
- Given the finite arithmetic sequence: 5; 1; -3; ...; -83; -87
- Solve for x: