Trigonometric Functions

Let the range of the function f(x)=6+16 x ( 3-x ) ( 3+x ) 3x 6x, x be [ , ]. Then the distance of the point ( , ) from the line 3x+4y+12=0 is :

1. 11
2. 10
3. 8
4. 9

Answer

(1) 11

Solution

x ( 3-x ) ( 3+x )= 14 3x f=6+4 3x 3x 6x=6+ 12x

Range [5,7]: ( , )=(5,7).

[figure]

d= |3(5)+4(7)+12| 32+42= 555=11

Answer: (1)