Find the directional derivative of f(x,y)=arctan(xy) at the point (-2,5) in the direction of maximum decrease. What is the Domain and Range of f(x,y)=arctan(xy)?
In the first 5 examples find the derivative of
Y
Y=epower2x
Y=epower-2x +xpower2
Y=epowerxpower1/2
Y= epower-3/x
Y=epower4xdivided by xpower2
Integrate the following
Int x epower5xpower2 dx
Int epower-2x between 1 and 0
Int.epower x1/2 divided by xpower1/2
Let arcman(y) = arcsin(y) - arctan(y). Find range and
domain of arcman(y). Prove that y=man(z) exists when z=arcman(y).
And find third order Taylor polynomial for arcman(y) and
man(z).
sketch the polynomial y=3x4-6x2
a) intervals for the function is increasin or decreasing
b) First Derivative test for relative extrema
c) Intervals for which the function is concave up or concave
down
d) Inflection Points
e) Sketch the graph. Label Key Points
2. Find the following derivative y=4x?
3. Find any maximum or minimum values of the function y(x)=1+x/e4x. Use a sign chart or a second derivative test to verify the answer(s) you get is a max or min.