Question

Suppose that f is a function with f2=-1 and f'2=-32. If hx=1/f(x)^12 then h'2=

Answer 1

We have
\[ h(x)=\frac{1}{{f(x)}^{12}}\]
Let's find h'(x)
\[ h'(x)= -12 \times {f(x)}^{-13} \times f'(x)\]
h'(2), let's substitute x=2 in h'(x)
\[ h'(2)= -12 \times {f(2)}^{-13} \times f'(2)\]

We have f(2)=-1
and f'(2)=-32
\[ h'(2)= -12 \times {-1}^{-13} \times -32\]
we know \({(-1)}^{-13}=-1\)
so
\[h'(2)=-12\times -1 \times -32= -384\]

Answer 2

thanks i got it now

Answer 3

Welcome dd