1) Find the intervals of increasing and decreasing for f(x) =
2x3 – 4x2.
2) Find the local minimum and maximum points, if any,
of
f(x) = 2x3 – 15x2 + 36x – 14. 3) Find the inflection points, if
any, of f(x) = 2x3 – 15x2 + 36x – 14. Give the intervals of
concavity upward and downward for f(x). 4) Find the absolute
maximum and minimum of f(x)= 2x3 – 15x2 + 36x – 14 on the interval...
1. Find the absolute minimum and maximum value of f(x) = x4 −
18x 2 + 7 (in coordinate form) on [-1,4]
2. If f(x) = x3 − 6x 2 − 15x + 3 discuss whether there are any
absolute minima or maxima on the interval (2,∞)
show work please
(a) For f(x) = 1 4 x 4 − 6x 2 find the intervals where f(x) is
concave up, and the intervals where f(x) is concave down, and the
inflection points of f(x) by the following steps:
i. Compute f 0 (x) and f 00(x).
ii. Show that f 00(x) is equal to 0 only at x = −2 and x =
2.
iii. Observe that f 00(x) is a continuous since it is a
polynomial. Conclude that f 00(x)...
f(x) = x4 − 128x2 + 7
(a) Find the intervals on which f is increasing or
decreasing. (Enter your answers using interval notation.)
increasing
decreasing
(b) Find the local maximum and minimum values of f. (If an
answer does not exist, enter DNE.)
local minimum value
local maximum value
(c) Find the intervals of concavity and the inflection points.
(Enter your answers using interval notation.)
concave up
concave down
inflection point
(x, y) =
(smaller x-value)
inflection point ...
1. Find Taylor series centered at 1 for f(x) = e^ (x^2). Then
determine interval of convergence.
2. Find the coeffiecient on x^4 in the Maclaurin Series
representation of the function g(x) = 1/ (1-2x)^2