Let f x = x − 2 2 e x / 2 . Given that f ′ x = 1 2 x 2 − 4 e x / 2 , f ″ x = 1 4 x 2 + 4 x − 4 e x / 2 determine the following properties of the graph of f . (a) The horizontal is ________ . (b) The graph is above the x -axis on the interval ________ . (c) The graph is increasing on the interval ________ . (d) The graph is concave up on the graph is ________ . (e) The relative minimum point on the graph is ________ . (f) The relative maximum point on the graph is ________ . (g) Inflection points occur at x = ________ .
Let f x = x − 2 2 e x / 2 . Given that f ′ x = 1 2 x 2 − 4 e x / 2 , f ″ x = 1 4 x 2 + 4 x − 4 e x / 2 determine the following properties of the graph of f . (a) The horizontal is ________ . (b) The graph is above the x -axis on the interval ________ . (c) The graph is increasing on the interval ________ . (d) The graph is concave up on the graph is ________ . (e) The relative minimum point on the graph is ________ . (f) The relative maximum point on the graph is ________ . (g) Inflection points occur at x = ________ .
Let
f
x
=
x
−
2
2
e
x
/
2
. Given that
f
′
x
=
1
2
x
2
−
4
e
x
/
2
,
f
″
x
=
1
4
x
2
+
4
x
−
4
e
x
/
2
determine the following properties of the graph of
f
.
(a) The horizontal is
________
.
(b) The graph is above the x-axis on the interval
________
.
(c) The graph is increasing on the interval
________
.
(d) The graph is concave up on the graph is
________
.
(e) The relative minimum point on the graph is
________
.
(f) The relative maximum point on the graph is
________
.
(g) Inflection points occur at
x
=
________
.
Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .
Sketch the graph of y = sin (x − c) for c = −π/4, 0, and π/4. How does the value of c affect the graph?
Use the graph shown to identify the activity of f(x),f '(x), and f "(x) at the given points.
ba Point D a. f> 0, f = 0, f 0
a Point G
c. f> 0, f'>0, f = 0
dB Point B d. f<0, f'=0, f"=0
y = f(x)
D
F
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY