This Demonstration shows the instantaneous rate of change
for different
values for polynomial functions of degree 2, 3, or 4, an exponential function, and a logistic function.
Choose the logistic function. Check the first derivative box. Find an approximate
value where the increase of
is highest.
Choose the exponential function. Check the second derivative box. Find an approximate
, the inflection point, where the tangent line switches from above the function to below. Actually, it is the zero of
.
Choose the polynomial of degree four. Check both the first derivative and second derivative boxes.
How big is
when
has its local maximum and local minimum?
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