Question

2)Find the value of x such that f(x) is decreasing function. f(x) = 2x ^ 2 - 15x ^ 2 - 84x - 7​

Answer 1

Answer:

f(x) = 2x³ - 15x² - 84x - 7

.: f'(x) = 6x²- 30x - 84

= 6(x² - 5x - 14)

= 6x²- 7x + 2 x - 14) =

= 6(x-7)(x + 2)

f(x) is an decreasing function, if f'(x)

< 0

. 6(x - 7)(x +2)< 0

:: (x - 7)(x + 2) < 0

ab <0 a > 0 and b<0 or a <0 or

b>0

: Either (x - 7) > 0 and (x + 2) <0 or

(x - 7) < 0 and (x + 2) > 0

Case 1: x -7 > 0 and x + 2 <0

.: x > 7 possible.

and x<-2, which is not

Case 2: x -7< 0 and x+ 2> 0

..X<7 and x>-2

Thus, f(x) is an decreasing function

for 2 < x < 7 i.e., (-2, 7).