If f (x) = 3x +7, find: f(3) = [ ? ]

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

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Q: The derivative of f(x) = 3 (22 + 4x) is - O 3x + 12 O -3x-2(2x + 4) 3x-2(2x + 4) O 3 -3x-3 (2x + 4)

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Q: If I have f^-1=2x-4 how can I find f(x)?

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Q: Find the second derivative of the function.        f(x) = 4x5 − 2x3 + 5x2

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Q: Find the second derivative of the function. f(x) = 4x3/2

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Q: Find the quotient x+h)-f(x) for f(x) = 7x – 3x²

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Q: Find f(-3) for f(x) = x² – 3x + 3

A: Given f(x)=x2-3x+3 To find f(-3) we put x=-3 in the above function.

Q: find the derivative  f(x)= (2x-3)6(3x+4)

A: Given function is f(x)=(2x–3)^6(3x+4). Formulas used:

Q: The derivative of f(x) 4 (x2 + 3x) is O -4x3 (2x + 3) -4x 2(2x + 3) 4 O 4a-2(2x + 3) 4.x + 12

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Q: Find the second derivative. f(x) = 5x10 - 19x5 – 11x3 + 2 f"(x) =

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Q: How is the graph of f (x) = x3 − 12x2 + 36x − 16 related to the derivative f'(x) = 3x2 − 24x + 36?

A: We have been given the equations f (x) = x3 − 12x2 + 36x − 16 and the equation of the derivative…

Q: Find the domain of f(x)=ln(4x-20)+ln(x 2+9x+18)

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Q: x + 3 f(x) : x2 - 3x - 18 :--Select-- -Select---

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Q: 2. f(x) = 9x2 - 1 at x = 1

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Q: Find the extreme values of f(x) = 5 - 2r2, IS1 lx+ 2, x> 1.

A: Given function is defined in two intervals  So firstly we will discuss  for  x≤1 f(x)=5-2x2 we have…

Q: For f(x) = (2a* + 3x)(5x*), find the derivative of f(x). 80x7+ 60x3 20x7-30a3 O 10z8 + 15x4 O…

A: We will use concept of differentiation to solve this.

Q: Differentiate the function f(x) = In(6x7 – 4x) + v2 – e3x. - -

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Q: Find the third derivative of the function f(x)=2x5-7x4+4x2-8x+11.

A: on doing diffrentiation with respect to x we will get

Q: . Find the first, second, and third derivative of function f(x) = 3x5 – 2x³.

A: Topic:- derivatives

Q: Find f'(x) using the rules for finding derivatives 4x2 - 5x + 2 f(x) = 3x +7

A: We have to find

Q: Find (fo g)(-2) when f(x) = - 4x -4 and g(x) = 9x +3x- 2.

A: Here, the given functions are: f(x)=-4x-4,g(x)=9x2+3x-2

Q: What happens to the values of f(x)=(x2-2x-3)/(x2-3x) as x ->0 ?

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Q: find the derivative f(x)=(2x3-3)2/3

A: Consider the given function

Q: If f(x) = 6 + 7x – 2x?, find f'(2). -

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Q: Find the derivative:   f(x) = (4x3-7x+9)5

A: Given:  fx=4x3-7x+95 To Find: The derivative of the given function

Q: iven the function y=2x³-4x²+5,

A: Given, the function               y=2x3-4x2+5

Q: If f(x) = 2x^2 - 10x - 33 , what would the derivative f’(x) be?

A: Given : fx = 2x2-10x-33

Q: calculate the derivative. f (x) = 4x5/3 − 3x−2 − 12

A: To find the derivative of: f(x)=4x53-3x-2-12 Solution: f(x)=4x53-3x-2-12 Differentiating both sides…

Q: 4 Find the value of f'(-1) if ƒ (x) =. (3xr² – 2x +1)

A: we have : f(x) = 4(3x2-2x+1)3 To find :f'(-1)

Q: Find the derivative of the functionf(x)= 9x² + 4x +6, using the definition of the derivative,

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Q: Find the second derivative of the function. f(x)= [3x3+7]7

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Q: Find the derivative f(x) = √(7 + 4x2) - (1)/(5x2 + 9).

A: Consider the provided function, fx=7+4x2-15x2+9 Find the derivative of the function.…

Q: Calculate the derivative. f (x) = 4x5/3 − 3x −2 − 12

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Q: What value of b completes the function f(x) = −x2 + bx + 1?

A: We have to find the value of b that completes the function f(x)=-x2+bx+1.

Q: Find the derivative of f. f(x) = 3x4 + 8x3

A: f(x)=3x4+8x3differentiating both sides w.r.t. xf'(x)=34x3+83x2f'(x)=12x3+24x2

Q: The derivative of is f (x) = 3x* + 7x² + 5x + 2 %3D

A: Given, f(x) = 3x4 +7x2 +5x +2

Q: Find the second derivative of the polynomial function y=3x4−2x3+4x2−5x+1.

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Q: 6. If f(x) = 10x – 5, what is f-1(ƒ (3))?

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Q: Find the derivative of the function. g(x) = 8/ (5x2-6x)4

A: To find the derivative of the function

Q: Let f(x) = 2x² – 12x + 3. For what x-value isf' (x) = 0? x =

A: To find: The values of x at which f'(x)=0. Given information: The function is f(x)=2x2-12x+3.…

Q: Find the inflexion point(s) of f(x) = x²-3x²³

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Q: If f(x) = 5 + 4x – 2x?, find f'(4).

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Q: For k(x)=(−3x2+2x−3)(x−2)(−x+3), find the derivative of k(x) using the product rule.

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Q: Find the derivative of the function. f(x)=6x2(9-8x)4

A: Use the product rule of differentiation: fx=ux.vxf'x=u'x.vx+ux.v'x

Q: For k(x)=(3x+2)(−x+2)(−3x2+x+1), find the derivative of k(x) using the product rule.

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Q: Find the extreme values of the function f(x) = (x² + 2x)³ on the interval [-2, 1].

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Q: Use the definition of the derivative to solve.

A: To determine the derivative of the function.

Q: - f(x) = 4x² – 10z + 11, 0 < ¤ < 7.

A: fx=4x2-10x+11;0≤x≤7 Differentiate the above function with respect to x. f'x=ddx4x2-10x+11=8x-10…

Q: Calculate the derivative. f (x) = 2x3 − 3x2 + 5

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Q: If f(x) = 4x? 10x – 40, find f'(x). - -

A: Given function is, f(x)=4x2-10x-40 we know that, ddxxn=nxn-1andddxaf(x)=af'(x)

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.