6. let ( f ) be differentiable function and ( f(3)=4, f^{prime}(3)=5, f^{prime}(4)=6 ). what is (…

6. let ( f ) be differentiable function and ( f(3)=4, f^{prime}(3)=5, f^{prime}(4)=6 ). what is ( left(f^{-1}\right)^{prime}(4) )? your answer:

6. let ( f ) be differentiable function and ( f(3)=4, f^{prime}(3)=5, f^{prime}(4)=6 ). what is ( left(f^{-1}\right)^{prime}(4) )? your answer:

Answer

Explanation:

Step1: Recall the formula for the derivative of an inverse function

If (y = f(x)) and (x = f^{-1}(y)), then ((f^{-1})^\prime(y)=\frac{1}{f^\prime(x)}) where (y = f(x)).

Step2: Identify the value of (x) for the given (y)

We are given (y = 4) and (f(3)=4). So when (y = 4), (x = 3).

Step3: Apply the formula

Using the formula ((f^{-1})^\prime(y)=\frac{1}{f^\prime(x)}), substitute (y = 4) (so (x = 3)) and (f^\prime(3)=5). Then ((f^{-1})^\prime(4)=\frac{1}{f^\prime(3)}).

Answer:

(\frac{1}{5})