Explain how to do these questions~

Question

1. An object moves in a straight line with its position at time t seconds given by s(t) = 3-2t+t^2, where s is the measured in metres. At what time is the object not moving?

2. Determine the coordinates of the point(s) on the graph of y=3x- 1/x at which the slope of the tangent is 7.

Answer 1

s=3-2t+t^2
ds/dt=-2+2t

when it is not moving, ds/dt =0, solve for t.

y=(3x-1)/x= 3-1/x

dy/dx=+1/x^2

if slope is 7, then
7=1/x^2
x^2=1/7
x= sqrt(1/7)
y=(3x-1)/x solve for y.

Answer 2

For number one we find the derivative of 3-2t+t^2

wouldn't that be t-2?

Answer 3

Oh crap nvm!

Answer 4

So for number 1 the answer is t=1

-2+2t=0
2t=2

2/2=1