plugging in the value of x that makes y equal to a: = = 1.
6. 1
First, we take the derivative of y: = . Next, we find the value of x where y = 0 : ln x = 0.
You should know that x = 1 is the solution. Now we can use the formula for the derivative of
the inverse of f(x): , where f(a) = c. This formula means that
we find the derivative of the inverse of a function at a value a by taking the reciprocal of the
derivative and plugging in the value of x that makes y equal to a.
SOLUTIONS TO PRACTICE PROBLEM SET 16
1. 5.002
Recall the differential formula that we use for approximating the value of a function: f(x + ∆x)
≈ f(x) + f′(x)∆x. Here we want to approximate the value of , so we’ll use f(x) =
with x = 25 and ∆x = 0.02. First, we need to find f′(x): . Now, we plug into the
formula: f(x + ∆) ≈ ∆x. If we plug in x = 25 and ∆x = 0.02, we get
(0.02). If we evaluate this, we get ≈ 5 + (0.02) =
5.002.
2. 3.999375
