w(t)= f(t)/(c+t)

Question

w'(t)=?

I got f'(t)(c+t)-f(t)/(c+t)^2 as the derivative and I'm having a hard time trying to prove that f(t_0) = f'(t_0) (C+t_0)

Help is always appreciated :)

Answer 1

Correct answer?

Quotient Rule for Derivatives:

[ f ( t ) / g ( t ) ] ´ = g ( t ) * f ´( t ) - f ( t ) * g ´( t ) / g ( t ) ^ 2

In this case g ( t ) = c + t so:

w ( t )´ = [ ( c + t ) * f´( t ) - f ( t ) * ( c + t )´ ] / ( c + t ) ^ 2 =

[ ( c + t ) * f´( t ) - f ( t ) * ( 0 +1 ) ] / ( c + t ) ^ 2 =

[ ( c + t ) * f´( t ) - f ( t ) * 1 ] / ( c + t ) ^ 2 =

[ ( c + t ) * f´( t ) - f ( t ) ] / ( c + t ) ^ 2

What (t_0) = f'(t_0) (C+t_0) mean?

Answer 2

it is assumed that f is differentiable and that w has an absolute maximum at t0

Show that f(t0) = f′(t0)(C + t0).