If f'(x) = x(x- 2)(x+1), then the graph of f has points of inflec- tion when x = A. -2 and 1 B. 2 and -1 C. 2 and 0 D. -2 and 0 E. 0, 2 and -1

Q: 3x-4 1. y = Arctan

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 derivative of the function by the limit process. f(x) = 1/(x − 1)

A: We use the limit definition of the derivative

Q: Please provide me with the solution to this problem. Please show the work and try to dumb it down so…

A:

Q: Find the derivative of the function by the limit process.

A: Given: fx=x2+x-3 To Find: The derivative of the given function by the limit process

Q: 17) Find the first derivative of f(x) = (cos4x)6 6 or f(x) = cos 4x

A:

Q: find the function with the given derivative whosegraph passes through the point P. ƒ'(x) = 2x - 1,…

A:

Q: Give an example of a function f (x) that has one  positive derivatives on the range (−1, 0) and a…

A:

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: The 2nd derivative of the given functions is 3 ponts y = 3 cos (4x- 5) None of the above -48 cos…

A:

Q: Find all possible functions f with the given derivative. f'(x)= 1/x-1, x is greater than 1

A: Obtain the all possible functions as follows.

Q: 2. Find y' if y = 5x + 2 using the limit definition derivative.

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: 1.f(0) = (금x* + 3)" %3D

A:

Q: Give an example of a function f (x) that has one positive derivative on (−1,0) and a negative…

A:

Q: To investigate these values, we find the second derivative f"(x) = %3D At the positive critical…

A: Given function is : fx=3x-4x3

Q: Find the derivative by the limit process. f(x) = 14-x²

A:

Q: Find an equation of the tangent line to the graph of f at the given point.

A: The equation of the tangent line to the graph of f at a given point x0,y0 is y-y0=f'(x0,y0)x-x0…

Q: Find the derivative of the function by the limit process.

A: Given: fx=x3-12x

Q: Find the derivative of the function.

A: Consider the given function as y=xtan-12x-14ln1+4x2

Q: The second derivative of a function is equal to 1. If the graph of the function passes through (0,2)…

A:

Q: Find the derivative of the function by the limit process. f(x) = x2 − 5

A: Given function is By limit definition of the derivative

Q: Suppose that the second derivative of the function y = ƒ(x) is y′′ = (x + 1)(x - 2). For what…

A: For inflection point we must have y" = 0

Q: Suppose that the first derivative of y = ƒ(x) is y' = 6(x + 1)(x - 2)2. At what points, if any, does…

A: Given the first derivative is: y'=6x+1x-22

Q: Suppose that the first derivative of y = ƒ(x) is y'= 6x(x + 1)(x - 2). At what points, if any, does…

A: The derivative of the function y=f(x) is y'=6xx+1x-2. We have to find at what points, if any, does…

Q: Find a function with the given derivative whose graph passes through point P f'(x)= 2xx+1-cosx,…

A: To determine the antiderivative satisfying the given initial condition

Q: Find the derivative of the function by the limit process. f(x) = x3 − 12x

A:

Q: 5) Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.…

A: The objective is to explain the reason definition of numerical derivative doesn't exist at x=2 in…

Q: the value of x at which the FOC is satisfied give us the ........(maximum/minimum) of the function…

A:

Q: Find the derivative of the function by the limit process. 7 f(x): x - 9

A: Given,          The function is fx=7x-9.

Q: Find the function ƒ(x) whose derivative is sin x and whose graph passes through the point (0, 2).

A:

Q: Calculate the first derivatives of ƒ(x) = x2/(x2 + 1) and g(x) = -1/(x2 + 1). What can you conclude…

A:

Q: Find the equation of the tangent line to the function f(x) = x² – 2 at the point (1,-1). You must e…

A: Given, fx = x4 -2  We have to find the equation of the tangent line to function at the point 1, -1.

Q: Find the derivative of the function by the limit process. f(x) = 7

A: The given function f(x)=7. The derivative of the limit  for the function f(x) is defined by So, to…

Q: The graph of a particular function passes through the point (3,4). Its first derivative is 2yy' + 2x…

A:

Q: equation of the function f whose graph passes thro f'(x) = x/25 - x²

A:

Q: Find the derivative by the limit process. f(x) = 13 – x2

A: Given that: f(x)=13-x2

Q: Find the derivative of the function by the limit process. f(x)=x2+x-1

A:

Q: A company has identified that the revenue R for a particular product is given by the equation R(x)…

A:

Q: Find the derivative of f ( x ) = 6 sin ^2 ⁡( x ) + 6 cos^2 ⁡( x ) at x = -6.5

A:

Q: If the average rate of change of q (x) in the period (5,7) is equal to 8 and y (5)*y (7) = 16 and f…

A:

Q: Find a function with the given derivative whose graph passes through point P f'(x)=1/x+2, x is…

A: The derivative is given as

Q: Find the derivative of the function by the limit process. f(x) = x3 − 2x + 1

A: Given function is fx=x3-2x+1. From the definition of derivative, we have f'x=limh→0fx+h-fxh Using…

Q: The function whose derivative is given by f'(x)=(x-¹), x 2. What is the #+2 critical point of f?

A: Critical point of a function is a point where either the derivative of function is zero or not…

Q: Find the derivative of the function by the limit process. f(x) = x3 - 9x + 1 f'(x)

A: We know,f'(x) = limh→0 f(x+h) - f(x)h  by limit processHere,f(x) = x3 - 9x + 1So,f(x+h) = (x+h)3 -…

Q: find the derivative by the limit process. f(x)=14-x^2

A: Here we find the derivative by the limit process fx=14-x2

Q: 2 12. f (x) = (1tsinx) Cosx

A:

Q: A company has identified that the revenue R for a particular product is given by the equation R(x) =…

A:

Q: Suppose that the second derivative of the function y = ƒ(x) is y'' = x2(x - 2)3(x + 3). For what…

A: Given that, y=f(x) Second Derivative is y'' = x2(x - 2)3(x + 3). As we know that, Inflection point…

Q: Find the function f(x) whose derivatives is sin x and whose graph passes through the point (0,2).…

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.