Question

(i) Test the curve y = x4 for points of inflexion ?
(ii) Show that the points of inflexion of the curve y2 = (3-47 (2-6) lie on the straight line
3x + Q = 46.

Answer 1

Answer:

y=x4−6x3+12x2+5x+7

y(x)=4x3−18x2+24x+5

y(x)=12x2−36x+24

y(x)=0

12x2−36x+24=0

x2−3x+2=0

x2−2x−x+2=0

x(x−2)−1(x−2)=0

(x−1)−1(x−2)=0

(x−1)(x−2)=0

x=1,2

Inflection point of a function is where the function changes from concave up to concave down or vice-versa

x<1,f(x)>0

1<x<2,f(x)<0

x>2,f(x)>0

∵f(x) changes sign

∴ At x=1,2y=f(x) has inflection point 

At x=1,y=f(1)=19

At x=2,y=f(2)=33

Point of inflection (1,19);(2,33)