Review practice · Section 1 of 2

(i) Determine the turning-point coordinates for $y=-(x+a)(x+b)^2$, where a,b are constants.

(ii) Sketch it with axial intercepts and turning points labelled when(a)a>0,b<0; and (b)a<b<0.

$C:y=(x^2+3x+1)/(2x-1)$.

(i) Sketch C with axial intercepts, asymptotes and stationary points.5 marks

(ii) Add a suitable curve to deduce how many real roots $2x^4+6x^3+2x^2+2x-1=0$ has.3 marks

$C:y=(-9x^2+6x-1)/(x-1)$.

(i) Without a calculator, find the range of y for which no points lie on C.3 marks

(ii) Sketch C with turning points, axial intercepts and asymptotes.3 marks

Sketch $y=(2x^2+1)/(x-1)$ with all turning points, axial intercepts and asymptotes. Hence state the values of a for which $2x^2+1=a(x-1)\cos(bx+c)$, x≠1, has no real solution for all b,c.6 marks

$C:y=(x^2+2x+3)/(x+1)$.

(i) Find exactly the values of y for which C does not lie.3 marks

(ii) Sketch C with axial intercept, asymptotes and stationary points.3 marks

(iii) Add a sketch on−π≤x≤πto solve $3(x+1)\cos x-1=x^2+2x+2$.3 marks

· Techniques of Differentiation

$G:y=(2x^2+kx-1)/(x+1)$, where k is constant.

(i) Given no stationary point, show that k>1.2 marks

(ii) Given y=2 x+1 is an asymptote, show k=3 and sketch G.4 marks