Differentiation Past Paper Questions

Differentiation Past Paper Questions

CSEC

2018 Q5 P2

(a)  Given that  $y=x^3+2x^2-1$  , determine 

(i) the coordinates of the stationary points 
(ii) the nature of each stationary point 

(b) Differentiate  $y=2x\sqrt{\left(4-8x\right)}$   

2017 Q5 P2

(a) Differentiate the expression  $\left(1+2x\right)^3\left(x+3\right)$  with respect to x, simplifying you answer.

(b) The point (-2,0)  lies on the curve  $y=3x^3+2x^2-24x$  . Determine the equation of the normal to the curve at point P.
 

2016 Q5

(a) Find  $\frac{dy}{dx}$  given that  $y=\sqrt{5x^2-4}$  , simplifying your answer.

(b) The point P (1,8) lies on the curve with  equation  $y=2x\left(x+1\right)^2$  . Determine the equation of the normal to the curve to the point P. 

(c) Obtain the equation for EACH of the two tangents to the curve  $y=x^2$  at the points where y = 16.

2015 Q5 P2

(a) Differentiate the following expression with respect to x, simplifying your answer.

 $\left(2x^2+3\right)\sin\ 5x$  

(b) 
(i) Find the coordinates of all the stationary points of the curve  $y=x^3-5x^2+3x+1$ 
 (ii) Determine the nature of the each  stationary point in (i) above.

2014 Q5 P2

(a) The equation of a curve is  $y=3+4x-x^2$  . The point (3,6) lies on the curve. Find the equation f the tangent to the curve at P , giving your answer in the form ax + by +c =0, where a,b,c  $\in Z$  .

(b) Given that f(x)  $=2x^3-9x^2-24x+7$  .
(i) Find ALL the stationary stationary point f(x).
(ii) Determine the nature of EACH of the stationary points of f(x). 

2013 Q5 P2

(a) Given that  $y=x^3-3x^2+2\$  . Find

(i) the coordinates of the stationary points of y 
(ii) the second derivative of  y and hence determine the nature of EACH of the stationary points. 

(b) Differentiate  $y=\left(5x+3\right)^2\sin x\$  with respect to x, simplifying your result as far as possible. 

2012 Q5 P2

(a) Differentiate the following expression with respect of x, simplifying your answer.

 $\frac{3x+4}{x-2}$  .

(b) The point (2,10) lies on the curve  $y=3x^2+5x-12$  . Find the equations for
(i) the tangent to the curve at P.
(ii) the normal to the curve at P.