Chapter 6 Practice Test Flashcards
Given x^ 2 − y^ 2 = 1, find dy / dx by implicit differentiation.
dy/dx=x/y
Given xy = 5, find dy / dx by implicit differentiation.
−y / x
Given √x+1/√y=1, find dy/dx by implicit differentiation.
√y^3/x
Given cos (x + y) = sin x sin y, find dy / dx by implicit differentiation.
−sin(x+y)+cosxsiny/sin(x+y)+sinxcosy
Evaluate the following as true or false. If dx/dy=1/dydx=0,then the tangent line to the curve y=f(x) is horizontal.
false
Find all points on the curve y + x = x^ 2 + y^2 where the tangent line is horizontal.
(1/2,1+√2/2) and (1/2,1−√2/2)
Find all points on the curve ln (xy) = x^ 2 where the tangent lines are vertical.
None of the tangent lines are vertical.
Which of the following functions is its own inverse? In other words, for which of the following functions is f −1 (x) = f (x)?
f (x) = 1 / x
What is the inverse of f(x)=3 3√x+1/5?
f−1(x)=(5x−1/3)^3
What is the value of d/dx[f−1(x)] when x=2, given that f(x)=2x−4?
1/2
What is the value of d/dx(f−1(x)) when x=7/3, given that f(x)=x^5+1/3x^3+x and f−1(7/3)=1?
1/7
What is the value of d/dx[f−1(x)] when x=π, given that f(x)=2x+cos^2x and f−1(π)=π/2?
1/2
What does arcsin(√3/2) equal?
π / 3
What does arcsin (sin (5π / 4)) equal?
−π / 4
Solve the equation arccos (x ^2 − 2x + 2) = 0 for x.
x = 1
