i already responded to this here. do not double posts. it wastes people's time. in fact, i think i see Soroban working on this right now when he could be helping someone else
I have a calc test tomorrow, and as I was studying, there were some problems I couldn't figure out. Can anyone help me with these, please..?
1) Find the equations of the two tangent lines to the graph of that pass through the point (-2,-9)
2) Consider the curve defined by the equation for 0 less than or equal to y less than or equal to 2pi
a) find dy/dx in terms of y
b) Write an equation for each vertical tangent to the curve.
c) Find d^2y/dx^2 in terms of y
thanks so much for the help! i really need it, hehe:]
Hello, Adrienne!
1) Find the equations of the two tangent lines to the graph of
that pass through the point
Let the point of tangency be
The slope of the tangent is: .
At , the slope is: .
We want the slope of to equal .
The slope of is: .
Then we have: .
. . which factors: .
. . and has roots: .
The corresponding y-values are: .
We have two points of tangency: .
. . At , the slope is: .
. . At , the slope is: .
You can write the equations of the tangent lines now . . .
2) Consider the curve defined by the equation for
a) Find in terms of
b) Write an equation for each vertical tangent to the curve.
c) Find in terms of
a) Differentiate implicitly: .
Then: .
b) For a vertical tangent, the slope is undefined; its denominator is zero.
So we have: .
Substitute into the equation: .
c) We have: .
Then: .
Since , we have: .
Therefore: .