Help me with Calculus, please.

[SgtStedenko]

Ok I have this take home test in Calculus on derivatives and I was hoping to get some help.

Here a few problems, if you can do any of them and show me how you did them that would be great, my teacher sucks.

1. The velocity of an object at time t can be described by v=(t^2)(cos(2t+3)/(t^2+4t+1). Approximate the acceleration at time t=2.75.

My answer so far: Accelaration is the derivative of velocity and since the velocity is what v= we must find the derivative of that quotient. I think you we need to use the product rule, chain rule, and then the quotient rule. I think this is how ya do it? Right?

2. At what point(s) does the curve defined by x^2-6x=6-6y^2 have horizontal tangents. Multiple choice options: a=(3, (10^1/2)/2)* b=(3+15^1/2, 0)* c=(3, -((10^1/2)/2))* d=(3-15^1/2, 0)*

*15^1/2=square root of 15, 10^1/2=square root of 10.

Any help would be greatly appreciated.

 

[Vadatajs]

You're thinking is correct for #1, just triple-check your algebra and you should be fine.

#2, the tangent is horizontal when f'(x)=0 (should read f-prime(x)). Find the derivative of the given function, set it equal to 0, then solve for x. (or just look for points on the given curve that change from + to - slope, they might not be defined though).