For the following exercises, draw a graph that satisfies the given specifications for the domain x = [ − 3 , 3 ] . The function does not have to be continuous or differentiable. 218. f " ( x ) < 0 over − 1 < x < 1 , f " ( x ) > 0 , − 3 < x < − 1 , 1 < x < 3 , local maximum at x = 0, local maximum at x = ± 2
For the following exercises, draw a graph that satisfies the given specifications for the domain x = [ − 3 , 3 ] . The function does not have to be continuous or differentiable. 218. f " ( x ) < 0 over − 1 < x < 1 , f " ( x ) > 0 , − 3 < x < − 1 , 1 < x < 3 , local maximum at x = 0, local maximum at x = ± 2
For the following exercises, draw a graph that satisfies the given specifications for the domain
x
=
[
−
3
,
3
]
. The function does not have to be continuous or differentiable.
218.
f
"
(
x
)
<
0
over
−
1
<
x
<
1
,
f
"
(
x
)
>
0
,
−
3
<
x
<
−
1
,
1
<
x
<
3
, local maximum at x = 0, local maximum at
x
=
±
2
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 .
At a local college, for sections of economics are taught during the day and two sections are taught at night. 70 percent of the day sections are taught by full time faculty. 20 percent of the evening sections are taught by full time faculty. If Jane has a part time teacher for her economics course, what is the probability that she is taking a night class?
4.1 Basic Rules of Differentiation.
1. Find the derivative of each function. Write answers with positive exponents. Label your derivatives with
appropriate derivative notation.
a) y=8x-5x3 4
X
b)
y=-50 √x+11x
-5
c) p(x)=-10x²+6x3³
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
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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