) A course repeater claims that his brother who did some Calculus at college years ago, bu urrently on some cough medication, believes that the first derivative of is f'(x) = 2-1+집+3-전+1 [(2x² – 1)(x² + 3) (2x2 – 1)(x² + 3) x) = 4x 2х 2x x2 +1 x2 +1 nd (x² + 8)7 (2 – 3x2)5 sing the product, qoutient and chain rules you learnt in Unit 7 of this Course, could you 30x is g'(x) = 14x %3D at the first derivative of g(x): x² + 8 *2– 3x 2 – %3D - - onfirm whether his brother is right, wrong or a little tipsy.
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
![ined in Unit 1 and 2, verify whether the limit to infinity of n(n+ 1)(n+ 2)-(n+ 3)-1
is equal to one.
A
and that h(T) = T2-2T-7,find h(7).
(4) Given matrix A =
3
Problem Set D
1) A course repeater claims that his brother who did some Calculus at college years ago, but
currently on some cough medication, believes that the first derivative of
(2x2 – 1)(x² + 3)
(x) =
[(2x² – 1)(x² +3)]
x2 +1
4x
2x
2x
-is f'(x) =
x2 +1
I2x² – 1 * x² + 3¯ x² + 1
and
30x
(x² + 8)7
(x² + 8)7
(2– 3x2)5
Using the product, qoutient and chain rules you learnt in Unit 7 of this Course, could you
14x
hat the first derivative of g(x) =
is g'(x) = 2+8 2-3x²] [(2 – 3x²)³]
%3D
-
confirm whether his brother is right, wrong or a little tipsy.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F74b15041-4539-4143-b199-ee49b840ff49%2F254618cd-66de-42e6-8e63-3b3d6b4a9bea%2F3w1mfy9_processed.jpeg&w=3840&q=75)
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