4.
First, we take the derivative of y: = 1 + 3x^2 . Next, we find the value of x where y = −2: −2
= x + x^3 . You should be able to tell by inspection that x = −1 is a solution. Or, if you are
permitted, use your calculator. Remember that the AP Exam won’t give you a problem where it
is very difficult to solve for the inverse value of y. If the algebra looks difficult, look for an
obvious solution, such as x = 0 or x = 1 or x = −1.
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: = .
5. 1
First, we take the derivative of y: = 4 − 3x^2 . Next, we find the value of x where y = 3: 3 =
4 x − x^3 . You should be able to tell by inspection that x = 1 is a solution. Or, if you are
permitted, use your calculator. Remember that the AP Exam won’t give you a problem where it
is very difficult to solve for the inverse value of y. If the algebra looks difficult, look for an
obvious solution, such as x = 0 or x = 1 or x = −1.
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
