Expert: Socrates - 1/21/2008

Question
Hi,
Let f and g be twice differentiable functions such that f'(x)<=0 for all x in the domain of f. If h(x)=f(g'(x)) and h'(2)=4. What (if anything) can you say about f, g, and h at x = 2?
would I need to go reverse processing? -
Thanks!

Answer
You can't say anything about f,g and h at x = 2

Suppose a , b and c are any numbers and we let

f(x) = -x + a + 2

g(x) = -2x^2 + (a-c+10)x + b+2c-2a-12

then f and g meet the conditions of the problem with

h(x) = 4x + c-8


You can easily check that

f(2) = a

g(2) = b

h(2) = c

since a, b, c could be any numbers we care to choose , we can't say anything about f,g and h at 2.