calculus homework. but i don't get what the questions mean?

[tinalism]

you don't need to give me the accurate answer but i wish someone can give me the step/process of how to do when i have this kind of problems


**what am i supposed to do with the question? find the x = to? or y=? or change in tri identity? i am confused by the question itself >_<

1. x+cos(x+y)=0
2. sinx-cosy-2=0

**in a given distance, i know how to find the velocity and acceleration
the time i factor out =2

s=t^3-6^3+12t-8

but the question is

1. the minimum value of the speed is?
2. the speed of the particle is decreasing for?

how to find the speed?

**in a given function f(x) =x^2 -2x^3

find how many relative extremum, pt of inflection and relative extrema this function have

** this one is a word problem that i don't have a single clue

A smooth curve has the property that for all x the value of its slope at 2x is twice the value of its slope at x. the slope of the curve at x =0 is?

**slope problem

the slope of the tangent to the curve y^3x+y^2x^2=6 at(2,1) is?

 

[galactus]

For the last one, are you familiar with implicit differentiation?.

I assume you mean: \(\displaystyle xy^{3}+x^{2}y^{2}=6\)

\(\displaystyle 3y^{2}x\frac{dy}{dx}+y^{3}+x^{2}2y\frac{dy}{dx}+y^{2}2x=0\)

\(\displaystyle \frac{dy}{dx}(3y^{2}x+2yx^{2})+y^{3}+2xy^{2}\)

\(\displaystyle \frac{dy}{dx}=\frac{-y^{3}-2xy^{2}}{3y^{2}x+2yx^{2}}\)

\(\displaystyle \frac{dy}{dx}=\frac{-y^{2}(2x+y)}{xy(3y+2x)}\)

\(\displaystyle \frac{dy}{dx}=\frac{-y(2x+y)}{x(3y+2x)}\)

Now, plug in the x and y values:

\(\displaystyle \frac{-(1)(2(2)+1)}{(2)(3(1)+2(2))}=\frac{-5}{14}\)

 

[pka]

I am not quite sure of what we are to do with these?
1. x+cos(x+y)=0
2. sinx-cosy-2=0

There are solutions to both. But not sure of the method you are to use.

For #1: x=0 and \(\displaystyle y = \frac{{\left( {2k - 1} \right)\pi }}{2}\) for any integer k is a set of solutions.

There is also a solution if y=0 and −x=cos(x) (x~−0.774).

For #2; you need sin(x)=1 and cos(y)=−1.

 

[tinalism]

thanks for all ur help... i am trying to go with the process and study