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

abondantQ 2021-01-22 Answered
The table shows some values of the derivative of an unknown function f.Complete the table by finding the derivative of each transformation of f, it possible
a) g(x)=f(x)  2
b) h(x)=2f(x)
c) r(x)=f(3x)
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Expert Answer

ottcomn
Answered 2021-01-23 Author has 97 answers
Step 1
The derivative properties:
ddx(f(x)  a)=f(x)
ddx(af(x))=af(x)
calculate the derivative of g(x)=f(x)  2 with respect to x as follows
g(x)=ddx(f(x)  2)
=f(x)

Step 2
Now calculate the derivative of h(x)=2f(x) with respect to x as follows
h(x)=ddx=(2f(x))
=2f(x)
h(x)=2f(x)

Step 3
Now calculate the derivative of r(x)=f(3x) with respect to x as follows
r(x)=ddx=f(3x)
= 3f(3x)
As r(x)= 3f(3x), compute the the value of
3f(3x)
r(2)=3f[3 (2)]
=3f(6)
Here r(2)= 3f(6) cannot be computed the values
of f(6) is not known.
r(1)= 3f[3 (1)]
= 3f(3)
= 3(5)
=15
r(0)= 3f[3 (0)]
=3(13)
=1
And r(1)= 3f[3 (1)]
= 3f(3)
Hense 3f(3) can not be compluted.
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