Cracking The Ap Calculus ab Exam 2018

You need to use implicit differentiation to find .

6 x −   8   y   =   0

Now, instead of rearranging to isolate , plug in (2, 1) immediately and solve for the derivative.

6(2) − 8(1) = 0

Simplify: 12 − 7 = 0, so =

Be  smart   about   your    problem solving.    Just    because you can

simplify    something   doesn’t mean    that    you should. In  a   case    like

this,   plugging    into    this    form    of  the derivative  is  more    effective.

Getting the hang of implicit differentiation yet? We hope so, because these next examples are slightly
harder.

Example 5: Find the derivative of = −x at (1, 1).

First, cross-multiply.

2 x −   5y^2    =   −x  (4  y^3     −   x^2 )

Distribute.

2 x −   5y^2    =   −4xy^3  +   x^3

Take the derivative.

2   −   10  y   =   −4x     −   4   y^3     +   3x^2

Do not simplify now. Rather, plug in (1, 1) right away. This will save you from the algebra.

2 − 10(1) = −4(1) − 4(1)^3 + 3(1)^2