Use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3). f(x) = - 4 f'(x) =| (Simplify your answer. Use integers or fractions for any numbers in the expression.) f'(1) = (Type an integer or a simplified fraction.) f'(2) = (Type an integer or a simplified fraction.) f'(3) = (Type an integer or a simplified fraction.) %3D

Q: Find the derivative of f(x) = (1 + 2x²)(x – x²) in two ways: by using the Product Rule and by…

A: Given f(x)=(1+2x2)(x-x2) By Product rule,…

Q: Find the second derivative of the function. f(x) = 5x + 26x F"(x) =

A:

Q: Solve for the derivative of x² – y² = 9 using implicit differentiation %3D

A: Given :                x2 - y2 = 9To find :                 y'

Q: Find second derivative of f(x) =6x^2+7x+1

A: We have to find second derivative of  f(x) = 6x2+7x+1 Then , f'(x) = 12x + 7

Q: Find the second derivative of the function f(x) = 3*(square root of x+2 divided by 2x +1

A:

Q: 8. Find the derivative of f (x) = 2tanx – 3secx. Show all steps -

A: We have to find the derivative of the function fx=2tanx-3secx Then,…

Q: Find the second derivative. 9. f(x) = V4x-5 f"(x) = f'"(x)=|

A:

Q: Find the derivative of the function. 5 F(x) 1 + 4x + x3 F'(x) :

A:

Q: 5 Find the derivative of f (x) = (9x4 -

A: Consider the given: fx=9x4−7x5Find the derivative:f'x=ddx9x4−7x5

Q: Find the first derivative of f(x) =5x+6

A: We have to find first derivative of  f(x) = 5x+6

Q: 1. Find the first derivative by using the definition for f(x) = 3x² – 2x – 5, hence - find f'(-2)

A: Derivative of a function is ratio of difference in output and difference in input.

Q: 9. Use the 2nd derivative to find the inflection point for f(x) = x³ – 6x2 – 4x +3 %3D

A: We will find the point of inflection as following.

Q: Find the second derivative of the function f(x)= x^4 x sec(x)

A:

Q: Solve for the second derivative of f(x)=2x-2/x+5

A:

Q: Obtain the second derivative of the function f(x) = 6 In(8x) – 3z4 and state the value of this…

A:

Q: Find the second derivative and the points of inflection using the second derivative f(x) = ln(x) /…

A:

Q: Find the derivative of f (x) = 9x − 5 at x = 2 and x = 5.

A: The derivative of a function f(x)  at a point a  can be calculated by applying the value a   to the…

Q: How to find the critical points of this derivative

A: We have to find critical point of f(x),where f'(x) is given by:

Q: (x) = ,2x+1

A: Explanation and solutions is given below....

Q: Solve for the derivative of the function using chain rule. 11. f(x)= ln(sin(8x))

A:

Q: Find second derivative of f(x) = (4/x) +6x-5

A: We have to find second derivative of  f(x) = (4/x) + 6x - 5 Then ,  First derivative of f(x) is…

Q: Find the second derivative of the function. 8. f(x) = 4x3/2 9. g(x) = x-1 10. h(x) = sinx

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: 4x +2 x-12 7. f(x) = 2x

A:

Q: Find the derivative of f (x) = ln| x3 - 10x2 + 8| .

A: Given        f(x)=lnx3-10x2+8

Q: Find the equation of the line tangent to f(x)=3x2 +4x+5 at the point (0, 5)

A: Given : f(x) = 3x2 + 4x + 5 A point (0, 5)   To  find the equation of the tangent line.

Q: Find the relative extrema of the function f(x)= x2+3x+4 using first derivative test.

A: fx=x2+3x+4 To find extrema of function.

Q: Solve the derivative of f(x)=−1/√2 x +2x

A: Given- fx=-12x+2x To find- The derivative of the above function. Formula used- Using the power rule…

Q: What is the second derivative of f(x)=x^2lnx

A:

Q: 3. Find the derivative of f(x) = x2020 – 2019.x" – 7x3 – 9x + en".

A: To Determine: Find the derivative of f(x)

Q: If f(x) = x³ + find f"(-1).

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Find the indicated derivative. 8. f (x) = x* – 2x³ + x² – 4 x – 20 find f*(x). -

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Find the derivative y=ln(2x^3+6x-1)^3

A: y=ln2x3+6x-13 take derivative y'=ddxln2x3+6x-13 y'=12x3+6x-13ddx2x3+6x-13

Q: 1-x3+2Vx f (x) =

A:

Q: Find second derivative f(x) = 1/X2-9

A: Given that fx = 1x2-9To find :second dedivative of fx

Q: Find the first derivative of f (x) = 2* 2*

A:

Q: 6. 3. Find the derivative of: -2Vx++ 5x – 8

A:

Q: f(x) = 5x* – 6Vx² + 유+ 18 x7

A:

Q: Find the first derivative of ƒ(x) = 7x¹⁰² cot(x). 10 f'(x) =

A: Given :fx=7x10excotx

Q: Find the second derivative of f(x)=x^-2 when x=4

A:

Q: Find the second derivative of 2x^2 ln (1/x^2)

A:

Q: 2. Find the derivative of y = (5x³ + 2 x)tanx. %3D

A:

Q: 2) Use logarithmic differentiation to find the derivative (Vx + 3)(x – 7)5 f(x) : (x3 – 4) - -

A: Given function is fx=x+3x-75x3-4 Given function can be re-written as: y=x+3x-75x3-4 Taking logarithm…

Q: 2) Find the derivative of the function f(x) = 3x² by definition

A:

Q: Find the 2nd derivative with complete solution y = 3x + 5 / x^2 + 4

A:

Q: 7. y= ln 2x³ 5х-3

A: Explanation of the answer is as follows

Q: Find the 2nd derivative of f(x) = √2x-x²

A:

Q: Find the fourth derivative of  f(x)=7x+ln(x)−125x.

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.