Question

Over which interval does the function decrease the fastest?
f(x)=3√ (-x+2)
A. 3 11 years ago

Answer 1

@mathmath333

Answer 2

that is where the derivitive has the lowest value
\[f(x)=3 \sqrt{-x+2} = 3(-x+2)^\frac{ 1 }{ 2 }\]
so
\[f'(x)= 1.5(-1)(-x+2)^{-\frac{ 1 }{ 2 }} =-\frac{1.5}{\sqrt{ -x+2}}\]

The domain of \(f(x)\) is \((\infty, 2]\)
and
\[\lim_{x \rightarrow 2} f'(x)= -\frac{1.5}{\sqrt{ -x+2}}\rightarrow -\infty\]
so the interval that is closest to -2 and within the domain will be the one we are looking for
A and D are not fully in the domain
From B and C, B is closest to 2
So it must be B

Answer 3

Thank you @abtster