Consider the following functions. f(x)=x^(3)-8 and g(x)=\sqrt(x+1)   Find the domain for (fg)(x). Express your answer in interval notation.

Q: use the definition of derivative to find f prime (x). f(x)= 3(2x-1)^3

A: Given function is fx=32x-13. To find the derivative of the function using definition of derivative.…

Q: What is the derivative of the function f(x) = 2x + 3 at the number x = 4?

A:

Q: Apply the First Derivative Test to identify all relative extrema. f(x) = -7x³ + 21x +3

A: fx=-7x3+21x+3 Differentiating with respect to x, we get f'x=-73x2+211+0⇒f'x=-21x2+21 Now to find…

Q: Find the derivative of ƒ (x) = /7– 8x. %3D To enter va, type sqrt(a). f' (2) =

A: We have to find the derivative of the given function.

Q: Find all relative extrema of the function f(x) = x4 - 4x2 + 2 by using the Second Derivative.

A:

Q: Find the derivative of the functions f(x)=(2x2-1)(x3+3)

A: We can make it easier for you.

Q: please take the first and second derivative of this function:    cube root of x^2 - (1/cube root of…

A: First express the expression with exponents of x.

Q: Find derivative using product or quotient rule

A: f'(x)=((x2)'(x+3)(4x-1)-x2((x+3)(4x-1))')/((x+3)(4x-1))2       (Using quotient rule)…

Q: How do you find the 17th derivative of f(x)=2x^15-13x?

A: We can find the 17th derivative as below.

Q: Find the third derivative if the function. 15. f(x)= 1/x

A:

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: What is the slope of the line tangent to the graph of a function defined by f(x)= x² + √x at x=1?

A:

Q: Find invers of function f(x)=1/2x+1

A:

Q: Find derivative of f(x) = 5x+(7/x)

A: The function is fx=5x+7x.   Differentiate the function with respect to x.…

Q: sketch the graphof the function and state its domain. f (x) = 4 ln(x − 2) + 1

A: A function is usually represented as f(x) where x is the input to the function and f(x) represents…

Q: Use the definition of the derivative to solve.

A: Given,

Q: find the derivative of the function F(x)=4(x^3-x)^4

A: According to the given information, it is required to find the derivative of the given function.

Q: Find the derivative of f(x) = - 2 * root(4, x ^ 5) + 7/(x ^ 6)

A:

Q: Use the second derivative test to find the local extrema for the function. y = 3x5- 25x3 + 60x + 20

A: We can use the application  derivative in order solve the given problem.

Q: Write a derivative formula for the function fx)- 12.2(4.7 x2 1.5475x(4.7-2( 4.7*) f'(x) 12.2 = X

A: Given

Q: 17 Use the definition of derivative to evaluate the derivative of f(x) = 2x2 − 4

A:

Q: find the derivative of the function f(x) = 7(x^3-x)^4

A:

Q: Use the Quotient Rule to calculate the derivative. f (x) = (x+4) / (x2 + x + 1)

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: Find the derivative. 2 f(x) = 4√√8x² +9 f'(x) =

A:

Q: f(x) = (4x³ + 6x +1)°

A: To find the derivative of,  f(x) = (4x3 + 6x + 1)9

Q: Let f(x)=9−(4x^2+3x). Then according to the definition of derivative

A:

Q: Find the derivative of f(x) = (2x^2-x-1)(sqrt of x) %3D

A: A detailed solution is given below.

Q: Use the second derivative test to find the extreme values of the function 49 f(x) = 25x +

A:

Q: Use the definition of derivative to find f(x) = 2-x+2x^2

A: Given,          fx=2-x+2x2

Q: What is the derivative of a function f(x) = 4x³ – 3x2 at a number a? %3D

A:

Q: 6 (x+2)(x-5)(x²+7) V(x3-8)(x+3)(x+4) %3D

A: Using Logarithmic Differentiation.

Q: Find the fifth derivative of  f ( x) = 3 x 3 - 7 x 2 + 6. Use correct notation.

A:

Q: derivative of f(x)=2x^15-3^x, f^15(

A: We will find the required.

Q: Use the second derivative test to find the local extreme values of y= 2x7-x+12

A:

Q: Find the second derivative of the function f(x) = 8/(x − 2)2

A: Find the second derivative of the function f(x) = 8/(x − 2)2

Q: Apply the first derivative test to indentify all relative extrema. f(x) = ¹²-2x+1

A:

Q: What is the derivative of f(x)=4/3x^5/4 at the point x=4?

A: we using derivative nth degree formula to compute derivative

Q: Find the higher-order derivative    1. f ''(x)=16x^(3)-38x^(2)

A: Derivative

Q: How do you find the derivative of f(x)=5/1-8x using the definition of a derivative?

A: The given function is f(x)=51-8x

Q: What is the derivative for: X^3/(1-x^4)

A: What is the derivative for  x^3/(1-x^4)

Q: find derivative  f(x)= x3/square root of 1+x2

A:

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

A:

Q: What is the 1881th derivative of the function given by f(x)=1881x + 1923 at the point x=2020.

A:

Q: 13x

A:

Q: 9. Suggest a function that would have a derivative of f'(x) = 24x² + 6x – 10. Explain how you…

A: The derivative of a function id given as f'(x)=24x2+6x-10......(1)

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.