Questions involving implicit differentiation,

[slain4ever]

Homework Statement

Q1. using implicit diff to find dy/dx when x^2 y + 6xy^2 = 5x-2
Q2. Find max and min values of y= x^3 -3x^2 -6x + 7 on the interval -3<=x<=5
Q3.Find the exact values of the x coordinate of the points of inflexion on the graph of y = 2x^4 +3x^2 +x +5

Q4. a red car is traveling east from a point at 60kph while a blue car is traveling north away from the point at 60kph. if the red car is 3km from the point and the blue car is 4km from the point at what rate is the distance between the cars changing?

The Attempt at a Solution

Q1. ? no clue, differentiate each part separately or something like that

Q2. differentiate the equation substitute this into the quadratic formula and get two values (62.76 and 5.24) but according to this there is nothing that fits into the interval so i must have done it wrong.

Q3. Derive it twice, substitute into quadratic formula and find two value for x.. Then do something else which I am not sure of.

Q4. something to do with s^2 = x^2 + y^2 and deriving for ds/dt but I am not sure if this is correct or even how to do it.

Any help would be greatly appreciated.

 

[vela]

Homework Statement

Q1. using implicit diff to find dy/dx when x^2 y + 6xy^2 = 5x-2
Q2. Find max and min values of y= x^3 -3x^2 -6x + 7 on the interval -3<=x<=5
Q3.Find the exact values of the x coordinate of the points of inflexion on the graph of y = 2x^4 +3x^2 +x +5

Q4. a red car is traveling east from a point at 60kph while a blue car is traveling north away from the point at 60kph. if the red car is 3km from the point and the blue car is 4km from the point at what rate is the distance between the cars changing?

The Attempt at a Solution

Q1. ? no clue, differentiate each part separately or something like that

Sounds good. What do you get when you do that?

Q2. differentiate the equation substitute this into the quadratic formula and get two values (62.76 and 5.24) but according to this there is nothing that fits into the interval so i must have done it wrong.

Show your work. We can't really help if all you tell us is you got the wrong answer. Your approach is right. You just messed up the execution of it.

Q3. [STRIKE]Derive[/STRIKE] Differentiate it twice, substitute into quadratic formula and find two value for x.. Then do something else which I am not sure of.

What do you get for x when you do that? You don't have to do anything more. The points of inflection are where y''=0. The problem is asking you to find the values of x where that's true.

Q4. something to do with s^2 = x^2 + y^2 and [STRIKE]deriving[/STRIKE] differentiating for ds/dt but I am not sure if this is correct or even how to do it.

Any help would be greatly appreciated.

Yes, this is a good way to start. If x(t) is the position of one car on the x-axis and y(t) the other on the y-axis, s(t) is the distance between them, and ds/dt will be the rate of change of this distance, which is what you're being asked to find.

 

[rock.freak667]

Homework Statement

Q1. using implicit diff to find dy/dx when x^2 y + 6xy^2 = 5x-2

Let's start with this one. Yes you need to differentiate each one separately.

for 'x²y' use the product rule.


remember that when you differentiate y wrt x, you will get dy/dx

so if you differentiate y² wrt x you will get 2y(dy/dx)