Fiesta 8: Implicit Differentiation (www.ilearnmath.net) Fall 2009

AP Calculus | Fiesta 8|Shubleka  

Name_____________ Show all your work for full credit. Use the space provided below. Graphing calculators are not permissible. 1. Find y ' if sin( xy ) = x − y . 2. Suppose that we don’t have a formula for 2

g (2) = −4

g '( x ) = x 2 + 4

g ( x) but

for all

we know that:

x.

a) Use a linear approximation to estimate g (1.95) and g (2.05) . b) Are your estimates in part a) too large or too small? Explain. 3. Find f '( x) from first principles, that is, directly from the definition of the derivative. f ( x) =

4− x 3+ x

4. Find a parabola y = ax 2 + bx + c that passes through the point (1, 4) and whose tangent lines at x = −1 and x = 5 have slopes 6 and -2, respectively.