In each part, find the local quadratic approximation of f at x = x 0 , and use that approximation to find the local linear approximation of f at x 0 . Use a graphing utility to graph f and the two approximations on the same screen. (a) f ( x ) = sin x ; x 0 = π / 2 b f ( x ) = x ; x 0 = 1
In each part, find the local quadratic approximation of f at x = x 0 , and use that approximation to find the local linear approximation of f at x 0 . Use a graphing utility to graph f and the two approximations on the same screen. (a) f ( x ) = sin x ; x 0 = π / 2 b f ( x ) = x ; x 0 = 1
In each part, find the local quadratic approximation of
f
at
x
=
x
0
,
and use that approximation to find the local linear approximation of
f
at
x
0
.
Use a graphing utility to graph
f
and the two approximations on the same screen.
(a)
f
(
x
)
=
sin
x
;
x
0
=
π
/
2
b
f
(
x
)
=
x
;
x
0
=
1
Consider the function f(x) = x² + 4x – 5.
%3D
(a) Find the points, if any, at which the graph of each function f has a horizontal tangent line. (If an answer does not exist, enter DNE.)
V) = (|
(х, у) %3D
(b) Find an equation for each horizontal tangent line. (If an answer does not exist, enter DNE. Enter your answers as a comma-separated list of equations.)
(c) Solve the inequality f'(x) > 0. (Enter your answer using interval notation. If an answer does not exist, enter DNE.)
(d) Solve the inequality f'(x) < 0. (Enter your answer using interval notation. If an answer does not exist, enter DNE.)
(e) Graph f and any horizontal lines found in (b) on the same set of axes. (A graphing calculator is recommended.)
10
y
10
y
5.
-10
10
-10
10
-5
f
----
-10
-10
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.