Given: f (x) = (x − 2)/(x^2 − x +1)^2 a) Find the intervals
where f(x) is increasing, and decreasing b) Find the intervals
where f(x) is concave up, and concave down c) Find the x-coordinate
of all inflection points.
consider the function
f(x)=3x-5/sqrt x^2+1. given f'(x)=5x+3/(x^2+1)^3/2 and
f''(x)=-10x^2-9x+5/(x^2+1)^5/2
a) find the local maximum and minimum values. Justify your
answer using the first or second derivative test . round your
answers to the nearest tenth as needed.
b)find the intervals of concavity and any inflection points of
f. Round to the nearest tenth as needed.
c)graph f(x) and label each important part (domain, x- and y-
intercepts, VA/HA, CN, Increasing/decreasing, local min/max values,
intervals of concavity/ inflection points of f?
Given f(x) = 1 x 2 − 1 , f 0 (x) = −2x (x 2 − 1)2 and f 00(x) =
2(3x 2 + 1) (x 2 − 1)3 . (a) [2 marks] Find the x-intercept and the
y-intercept of f, if any. (b) [3 marks] Find the horizontal and
vertical asymptotes for the graph of y = f(x). (c) [4 marks]
Determine the intervals where f is increasing, decreasing, and find
the point(s) of relative extrema, if any....
Given f(x,y) =(x3y- 2x2y)
a) find the directional derivative of f(x,y) at (1, 2) in the
direction of <-3,4>
b)find the maximum value of directional derivative at (2,4) and
the direction in which this occurs
6) Given: (a) f (x) = (2x^2)/(x^2 −1) - Calculate f ′(x) and f
″(x) - Determine any symmetry - Find the x- and y-intercepts - Use
lim f (x) x→−∞ and lim f (x) x→+∞ to determine the end behavior -
Locate any vertical asymptotes - Locate any horizontal asymptotes -
Find all intervals where f (x) is increasing and decreasing - Find
the open intervals where f (x) is concave up or concave down