Question

Find the intervals in which the function f(x)=30-24x+15x2

-2x3

is

strictly decreasing.​

Answer 1

Answer:

f'(x) =-24+30x-6x²

Put f'(x)=0

-24+30x-6x²=0

Or -4+5x-x²=0

Or 4-5x+x²=0

(x-4)(x-1)=0

X=4,1

When x>4or

f'(x) >0

So f(x) is increasing in (4,infinity)

When x<0,

f'(x) <0

So f(x) is strictly decreasing in (-infinity, 0)