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February 21st, 2014, 04:45 AM   #1
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Some values of derivative of unknown function f?

The table shows some values of the derivative
of an unknown function f. Complete the table by finding
(if possible) the derivative of each transformation of f.
a) g(x) = f(x) -2
b) h(x) = 2f(x)
c) r(x) = f(-3x)
d) s(x) = f(x+2)


x - 2 -1 0 1 2 3
f'(x) 4 2/3 -1/3 -1 -2 -4
g'(x) - - - - - -
h'(x) - - - - - -
r'(x) - - - - - -
s'(x) - - - - - -

How to do this please? Can you tell me what to do and answer the first few boxes/blanks for me, so I can learn from them and do the rest? Thank you
shiseonji is offline  
 
February 21st, 2014, 05:53 AM   #2
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Re: Some values of derivative of unknown function f?

Quote:
Originally Posted by shiseonji
The table shows some values of the derivative
of an unknown function f. Complete the table by finding
(if possible) the derivative of each transformation of f.
a) g(x) = f(x) -2
b) h(x) = 2f(x)
c) r(x) = f(-3x)
d) s(x) = f(x+2)


x - 2 -1 0 1 2 3
f'(x) 4 2/3 -1/3 -1 -2 -4
g'(x) - - - - - -
h'(x) - - - - - -
r'(x) - - - - - -
s'(x) - - - - - -

How to do this please? Can you tell me what to do and answer the first few boxes/blanks for me, so I can learn from them and do the rest? Thank you
What, exactly, is your difficulty? If you are asked to do a problem involving derivatives, I would expect that you know some basic derivative properties:
(a) (f(x)+ g(x))'= f'(x)+ g'(x) and if g happens to be a constant, g(x)= c, its derivative is 0 so (f(x)+ c)'= f'(x).
(b) (cf(x))'= cf'(x) for c a constant.
(c) The chain rule: f(g(x))= f'(g(x))g'(x) and here g(x)= -3x.
(d) Chain rule again but now g(x)= x+ 2.
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