In Exercises 7 − 12 , sketch the graph of a function that has the properties described. f ( x ) defined only for x ≥ 0 , ( 0 , 0 ) and ( 5 , 6 ) are on the graph; f ' ( x ) > 0 for x ≥ 0 ; f ' ' ( x ) < 0 for x < 5 , f ' ' ( 5 ) = 0 , f ' ' ( x ) > 0 for x > 5 .
In Exercises 7 − 12 , sketch the graph of a function that has the properties described. f ( x ) defined only for x ≥ 0 , ( 0 , 0 ) and ( 5 , 6 ) are on the graph; f ' ( x ) > 0 for x ≥ 0 ; f ' ' ( x ) < 0 for x < 5 , f ' ' ( 5 ) = 0 , f ' ' ( x ) > 0 for x > 5 .
Solution Summary: The author illustrates the graph of the function f(x) using the first and second derivative rule and the given properties.
In Exercises
7
−
12
, sketch the graph of a function that has the properties described.
f
(
x
)
defined only for
x
≥
0
,
(
0
,
0
)
and
(
5
,
6
)
are on the graph;
f
'
(
x
)
>
0
for
x
≥
0
;
f
'
'
(
x
)
<
0
for
x
<
5
,
f
'
'
(
5
)
=
0
,
f
'
'
(
x
)
>
0
for
x
>
5
.
Determine whether the lines
L₁ (t) = (-2,3, −1)t + (0,2,-3) and
L2 p(s) = (2, −3, 1)s + (-10, 17, -8)
intersect. If they do, find the point of intersection.
Convert the line given by the parametric equations y(t)
Enter the symmetric equations in alphabetic order.
(x(t)
= -4+6t
= 3-t
(z(t)
=
5-7t
to symmetric equations.
Find the point at which the line (t) = (4, -5,-4)+t(-2, -1,5) intersects the xy plane.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY