All Tasks - Asymptote

Consider the function $f$, with domain $D_f = \left[0, 1\right]$, defined by $f(x)= \dfrac{\pi}{2} -2 \arcsin(1-2x)$. Let $r$ be the line tangent to the graph of the function $f$ at the point with abscissa $a$. It is known that line $r$ is perpendicular to line $x+4y=12$.

Give the missing coordinate p of the point P(2.2;p) in that way, that P is element of the graph of the linear function f with f: y = 4.4 - 0.5 x

The ride on an escalator can be described by the function f with f: y = -0.4 x + 6.6. Thereby x is in this equation the time for the ride in seconds, y the height in meter. A person takes the escalator to the next floor. The next floor is 3.5 m heigt. Estimate the time for the ride.

Solve the linear equation by equivalent transformation. 7x + 22 = 71

Let $f$ and $g$ be two differentiable functions in their domain, such that: $g(x)=-3\pi +2 \arccos(3f(x)+1)$, $f(1)=-\dfrac{1}{3}$ and $f^{\prime}(1)=\dfrac{2}{3}$. The reduced equation of the tangent line to the graph of $g$ at the point with abscissa $1$ is:

At the point of intersection with the ordinate axis, an equation of the straight line normal to the graph of the function $g(x)=2\arctan(x-1)$ is