Use the following table to determine the indicated derivatives or state that the

Question

Use the following table to determine the indicated derivatives or state that the derivative cannot be determined. (f^-1)'(0) (f^-1)'(6) (f^-1)'(-3) f'(-3) Choose the correct answer below and, if necessary, fill in the answer box within your choice. (f^-1)'(0) = (Type an integer or a fraction.) (f^-1)'(0) cannot be determined. Choose the correct answer below and, if necessary, fill in the answer box within your choice. (f^-1)'(6) cannot be determined. (f^-1)'(6) = (Type an integer or a fraction.)

Explanation / Answer

a)f(f-1(x))=x

differentiate on both sides

f '(f-1(x)) (f-1)'(x) =1

(f-1)'(x)=1/f '(f-1(x))

(f-1)'(0)=1/f '(f-1(0))

(f-1)'(0)=1/f '(-6)

(f-1)'(0)=1/2

b)(f-1)'(6)=1/f '(f-1(6))

(f-1)'(6)=1/f '(3)

(f-1)'(6)=1/(3/2)

(f-1)'(6)=2/3

c)

(f-1)'(-3)=1/f '(f-1(-3))

(f-1)'(-3) cannot be determined as f-1(-3) is undefined

d)f '(-3) =1/3 from the table

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