All Tasks - Asymptote

Consider the function f defined by $f(x)=x~arccot(2x+1)$. So df(0) is:

Consider the function defined by $f(x)=\frac{\pi}{4}-arccot(x)$. The tangent line of $f(x)$ for $x=1$ is $y=mx+b$ where (enter values to 1 decimal place)

Consider the function defined by $f(x)=-3\arccos(x+1)$. Determine the normal line of $f(x)$ for $x=-1/2$.

Hannah tees off a golf ball. The equation y=-5x^2 + 30x describes its flight height y (in m) as a function of time x (in s). Calculate the zeros of the function and explain what the zeros say about the flight of the golf ball.

The Italian Galileo Galilei discovered the law of gravity. The distance s in meters that a body falls in t seconds is approximately s = 5 t². He verified his law on the Pisa Sharp Tower, which is 54 m high (see picture). a.) How long does the stone fall from the top to the bottom? b.)From what height do you have to drop a stone so that it reaches the ground in 2s? Round to 2 decimal places.

The graph of the function f(x) = x² is translated and has the vertex S( -2/4). Cross the term of the new function.