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)?
Use the given function, its first derivative, and its second
derivative to answer the following:
f(x)=(1/3)x^3 - (1/2)x^2 - 6x + 5
f'(x)= x^2 - x - 6 = (x+2)(x-3)
f''(x)= 2x - 1
a) What are the intervals of increase and the intervals of
decrease
b) Identify local min and max points
c) What are the intervals where the function is concave up,
concave down and identify the inflection points
Question 1
Let f be a function for which the first
derivative is f ' (x) = 2x 2 - 5 / x2 for x
> 0, f(1) = 7 and f(5) = 11. Show work for all
question.
a). Show that f satisfies the hypotheses of the Mean
Value Theorem on [1, 5]
b)Find the value(s) of c on (1, 5) that satisfyies the
conclusion of the Mean Value Theorem.
Question 2
Let f(x) = x 3 − 3x...