(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) f(x) = [(2x² – 1)(x² + 3) 2х + [2x² – 1 ' x² + 3 x² + 1] 4x 2х - -is f'(x) = x² +12 x² + 1 and (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 30x + [x² + 8 ' 2 – 3x²] 14x that the first derivative of g(x) is g'(x) = %3D (2· 3x²)5] confirm whether his brother is right, wrong or a little tipsy.

Q: Find the third derivative. f(x) = 6x9 – 8x6 f"(x) = %3D

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Q: If f(x) = √ 8x + 3, compute the first, second, and third derivative of f(x). f'(x) = f"(x) = = f"(x)…

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Q: If f(x): f'(x) = = f"(x) = = f"(x) = √6x + 5, compute the first, second, and third derivative of…

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Q: Find the derivative of f (x) = 3x2.e3x2 A 6x2. e3x2 + e3x² 3x2. e 3x² + 6x - e 3x2 ©) 18x3. e3x2 +…

A: Derivative

Q: if f(2) = 1, f'(2) = 3, g(2) = 3, and g'(2) = -1, then the derivative of f(x).g(x) evaluated at x =…

A: Given: f(2) = 1, f'(2) = 3, g(2) = 3, and g'(2) = -1

Q: If f(x) = (3x + 1)5, compute the second derivative f'(x) at x = 0. f"(0) =

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Q: Evaluate the 3rd derivative of y= x5Tan(x4) if x=4

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Q: If f(x) = 3 + x + ex , find ( f-1)' (4)     The derivative of the inverse in 4

A: The given function is,                  f(x) = 3 + x + ex We want to find the value of (f-1)'(4). We…

Q: Assume a function such that Y = (2x410)/(6x² + 5x). Obtain the first derivative. O f'(X) = (8x³ -…

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Q: The first derivative of f(x) = e5x*-6x will be A. (6-20x)e**-6x B. (20x 6) e5x*-6x C. (6+ 20x)…

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Q: If f(x) = -4x³ - 5x² − 3x + 7, compute the first, second, and third derivative of f(x) - f'(x) =…

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Q: Find the first derivative for the following function. g(x) = 4e3x*+2x %3D A. g'(x) = 4e3x*+2x +…

A: Given function: gx=4e3x5+2x Differentiate the above function w.r.t 'x' g'x=ddx4e3x5+2x

Q: If f(x) = = f'(x) = f"(x) = 4x 5x2 +7 compute the first and second derivatives of f(x).

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Q: Y=0.83x +0.0094x2 +0.000042x3 Take out derivative of the given function.

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Q: If f (x) = In (4a + 1), then its third derivative is f(3) (æ) = %3D

A: In this question, concept of derivative is applied. Derivative The derivative expresses the rate of…

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.