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?
f(x)=2x^4-5x^3-9x^2+32x-20
-Find the
A: Intercepts
B: equation of asymptote
C: local extrema
D: Inflection Point
E: All end behaviours and behaviours around the
asymptote
Given f(x) = x^4 - 4x^3
1) find the intervals on which f is increasing or
decreasing.
2) find the local maximum and minimum values of f.
3) find the intervals of concavity and the inflection points
a) Let f(x) = −x^4 − 4x^3 . (i) Find the intervals of
increase/decrease of f. (ii) Find the local extrema of f (values
and locations). (iii) Determine the intervals of concavity. (iv)
Find the location of the inflection points of f. (v) Sketch the
graph of f. (You can choose your own scale for the graph)
b) A farmer wants to fence in an area of 6 km2 in a rectangular
field and then divide it in half with...
Let f(x) = −x^4 − 4x^3.
(i) Find the intervals of increase/decrease of f.
(ii) Find the local extrema of f (values and locations).
(iii) Determine the intervals of concavity.
(iv) Find the location of the inflection points of f.
(v) Sketch the graph of f. (You can choose your own scale for
the graph)
Let f(x) = x^4 -
4x^3 - 18 x^2 + 77
a) a) Find all critical values of the
function. [10]
b) b) Find all intervals of increase and
decrease. [10]
c) Find all relative extrema.
Use the second derivative test.
Label each as a relative max.
or a relative min. [10]
d) d) Find on what interval(s) the function is
concave up and concave
down. [10]
e) e) Find all inflection point(s), if any, of the
function. [10]