Differentiate the following functions.
Look at the graph of with op .
Algebraically calculate the extrema of .
Algebraically solve: .
The line intersects the graph of in four points. calculate the slope in those points.
In a tidal area the water level (in meter) at time (in hours) can be described by . Here at 0:00 o'clock on a certain day.
Calculate the water level at 0:00 o'clock.
Using differentiation, calculate the times of the high waters that day. Why is it not really necessary to use differentiation?
Calculate . What meaning does this number have for the behaviour of the water level.
At what times does the water level change fastest?
Here you see part of the graph of with .
Use differentiation to find the two extrema of .
Compose an equation for the tangent to the graph of for .
Calculate in which point of the graph of the tangent has the smallest slope. What is this slope?
Study the graph of function with .
How many extrema does this function have on the interval ?
The power of the alternating current provided by power companies is proportional to the square of the voltage (in Volt). The alternating current is delivered with an effective voltage of V, a frequency of Herz (that is periods per second) and an amplitude of approximately V. The voltage as a function of time is a true sinusoid.
Compose a formula for assuming that .
For the power : . What value does the proportionality constant have here?
Algebraically calculate the extrema and zeroes of .
The graph of is a true sinusoid. Give a formula for this sinusoid.