Question

Find f−1′ (2) if f(x)=(x−4)¹/²
a) 0.25
b) 0.5
c) 1
d) 2

Answer 1

To find f−1′ (2) if f(x)=(x−4)¹/₂, we need to find the derivative of f(x) and then evaluate it at x=2. The answer is 0.5. Hence the correct answer is option B

Step-by-step explanation:

To find f−1′ (2) if f(x)=(x−4)¹/₂, we need to find the derivative of f(x) and then find its value when x=2.

Step 1: Find the derivative of f(x)
Using the power rule, differentiate f(x) = (x−4)¹/₂ to get f′(x) = 1/2(x−4)¹/₂−1/2(2)¹/₂.

Step 2: Evaluate f′(x) at x=2
Substitute x=2 into f′(x) to get f−1′ (2) = 1/2(2−4)¹/₂−1/2(2)¹/₂.

Solving this equation, we get f−1′ (2) = 0.5.

Hence the correct answer is option B