I'm not sure how to use the information given in order to find the derivative.

Question

1) Suppose R '(1) = 6.

(a) If f(x) = R(4x), find f ' (1/ 4) .

(b) If g(x) = R(x + 3), find g ' (−2).

(c) If h(x) = R (x/11) , find h ' (11).

So in all of these cases I am not sure what to do since the chain rule applies but only if the inner and outer derivative is known and I am only given R '(1) = 6. If you could just help me get started on these parts I think I could finish I just don't know how what is given and what is wanted connect together.

Answer 1

Save the R'(1)=6 for after you've computed the derivative. Also, don't plug anything in until after you've computed the derivative.

 

f'(x) = d/dx R(4x)

= R'(4x)*4              by the chain rule

 

When we plug in 1/4 we get

=R'(1)*4

= 6*4

= 24

 

Parts (b) and (c) are very similar.

 

I hope that helps.