Show that f(x)g(x) = (x – a)" Cmdn' -m- n'=0 m=0

Q: Find f'(a). f)t( 1 t² +4

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Q: Find f. f '(x) = √(x) (3 + 10x), f(1) = 11 f(x) =

A: Consider the given function as f'x=x3+10x,f1=11

Q: Find y as a real-valued function of tif y(5) 9, y'(5) = 9. = y = 49y" 140y + 100y = 0, -

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Q: Find the function f(x) if f'(x) = ex+ 2 +(3/x) and f(1) = 6

A: We have to find the integral of f'(x) to obtain f(x) Steps: 1. Integrate with respect to x 2. Apply…

Q: Find f. f'(x)  =√ x (6 +5x) ,f(1)  =10

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Q: 2. Determine f'(1) for the function f(x) = (8x – 6Vx5 + 3) (x² – 9x² +) -

A: A detailed solution is given below

Q: Let S(x) = 4x$ (x' – 6). Evaluate the following specific values of f: (A)(2) = (B) (4) =

A: The objective of the question is evaluate the values.

Q: Find f(x) if f'(x) =2/+.

A: The derivative of f(x) is given, so to find f(x) we need to integrate f'(x)=2x+5x6. The integration…

Q: 3) Let f(x)= 2x+3 . Calculate by definition f'(2).

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Q: Let f(x) = 3e7x+3 +e². ƒ'(0) = Enter the exact value.

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Q: Find f. (x+ 1) (b) f'(x) = f(1) = 5 3.

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Q: Find f(x) if f "(x) = x -3/2, f ' (4) = 1  and f(4) = 4.

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Q: Let c =8 If f (x) = ecsin(). Find f' (0)

A: Given c=8and f(x)=ec.sin(x)⇒f(x)=e8sin(x)

Q: Find f '(a) f(t)6t12 t 7

A: The given function is

Q: If f is the function f (x) = + 4/x, then f' (4)

A: The function is  f(x)=4x+4x

Q: Find f if f"(x) = 0, f(0) = 2, f'(0) = 1

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Q: Find f ′(a) f(t) = t^5 - 3t

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Q: 2. Find f'(x) for f(x) = x²e.

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Q: 3. Let f(x) = 4x3+ + 2vx-7. Find f'(x).

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Q: Find f′(x) if f(x) = lnx / x2

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Q: Let y= f (x) be a function with f (4)=12 and f(4)= 0.5.

A: We have to find

Q: Compute f'(a) algebraically for the given value of a. f (x) 2x – a2; a = -1 limp 0 (4 – h) = 0 limp…

A: The function is given by f(x) = 2x-x2; a =-1 To evaluate : f'(a) Formula Used : f'(a) = limh→0f(a+h)…

Q: find f'(t) for f(x)=x/8x-8

A: We will need the quotient formula to find f'(x) Assume u and v, then find u' and v'

Q: f(3.8) - If we knew that f"(x) < 0 on the interval (3.5, 4.5), would your estimate above be an…

A: We need to find f(3.8)

Q: Find f if f" (x) = 24x² + 2x + 10, f(1) = -7, f'(1) = -2. %3D f(x) =[ %3D

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Q: 1 If f(x) = compute f(2) and f'(2)

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Q: Let f(x) = /2 + 4x f'(1) = 6

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Q: Find f. f(x) = f"(x) = 8x³ + 5, f(1) = 6, f'(1) = 2

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Q: Suppose that er f(x) = x2 + 17 Find f'(1). f'(1) =

A:

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.