Recall the inverse function theorem: if f(x) has an inverse, and if f(a) = b and a = f⁻¹(b), then
f⁻¹(f(x)) = x ⇒ (f⁻¹)'(f(x)) • f'(x) = 1 ⇒ (f⁻¹)'(f(x)) = 1/f'(x)
⇒ (f⁻¹)'(b) = 1/f'(a)
Let b = 10. Then pick the function f(x) such that f(a) = 10 and f'(a) = -8 for some number a.
Answer:
x=0
Step-by-step explanation:
Answer:
Is to give us a range of values for our estimated population parameter rather than a single value or a point estimate.
Answer:the answer to this is 9
Step-by-step explanation:
Answer:
1 3/8
Step-by-step explanation:
Possible derivation:
d/dx(1/8 (-2 + 3 x))
Factor out constants:
= 1/8 (d/dx(-2 + 3 x))
Differentiate the sum term by term and factor out constants:
= 1/8 d/dx(-2) + 3 d/dx(x)
The derivative of -2 is zero:
= 1/8 (3 (d/dx(x)) + 0)
Simplify the expression:
= 3/8 (d/dx(x))
The derivative of x is 1:
Answer: = 1 3/8
