How does the function ƒ(x) = x2 - 1/x - 1 behave near x = 1?

Q: Find the derivative (f' (x)) of f(x) = Vx + 2 . %3D

A:

Q: Let f(x) = x2 – 2.x. Use the definition of the derivative to calculate f'(3) %3D -

A:

Q: Find the derivative of the f(x) = (x² + 1)³

A: To find the derivative of the function: fx=x2+13

Q: Find the derivative of the algebraic function.

A:

Q: Find the derivative of the function. f (x) = = 4 %3D 12 - 12 - x2 0 4

A:

Q: Find the second derivative of the function.

A: From the given data:

Q: Find the derivative of a function f(x)=(x^2+1)^3 (2x−1)^4 f ' (1) = ____

A:

Q: Find the first and second derivatives of the functio f(x) = x(x² + 4)2 %3D f'(x) = %3D f" (x) = %3D

A:

Q: Find all critical points of the function f(x) = x4 – x-

A: Critical point is 5/4 Explanation is given below

Q: Find the derivative of f(x) = e* (3x' - 4) %3D

A:

Q: Find the first and the second derivatives of the function. f(x) = (8x + 8)³ f'(x) = f"(x) =| %3D

A:

Q: The function f(x)=(x)/(x-1) is discontinous at x=1 because

A:

Q: Where is the function f(x) =| x | differentiable?

A: Given information: fx=x The function, after removing modulus function, y=x=x,      x>0=-x,…

Q: Differentiate. f(x) = - 2 e -X t'(x) = ]

A:

Q: Find the derivative of the function f(x) = 9x2 - 15x by the de f(r + h) - f(x) f'(x) = lim h>0

A: f(x)=9x2-15x

Q: Find the derivative of the algebraic function.

A: we have to find the derivative of the function f(x)=x41-2x+1

Q: Find the derivative of the function. f(x) = V5x + 4 f'(x) =

A:

Q: The best suitable method to approximate a zero of the function f(x) = e* – 1 is:

A: Given f(x) = ex - 1

Q: Is the function f(x)= x+|x|-1 differentiable at x=0.

A: Consider the given function:

Q: what is the second derivative of  f(x) = 3(3x^3+2x^2)^10

A: We first find the first derivative using the power rule and chain rule.…

Q: The best suitable method to approximate a zero of the function f(x) = e* – 1 is: |

A: Given,                 f(x)=ex-1

Q: Find the absolute maximum value of f(x) = x2 – 2x + 10 over the interval 0, 3 -

A: Find your answer below

Q: Find the first and second derivatives of the function. f(x) = √3x-7     f '(x)=   f ''(x)=

A:

Q: Find the derivative of the algebraic function.

A: The given function is fx=x41-2x+1.

Q: 2. Use the first and second derivatives to obtain sketches of the function below. 4x+2 f(x) = %3D…

A:

Q: Find the derivative of the function. 4 2x - x2 f(x) = %3D x2 - 6 f'(x) =

A: given,        fx=-x2-2x+4x2-6

Q: Find all the critical numbers for the function g(x) = % xª -- x3 - 5x?

A:

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

A:

Q: Find the second derivative of the function. f(x) = 5(2 − 7x)4   Show your work

A: y''=?

Q: Find the value k that makes the function continuous. kx + 14, х > 2 f (x) = 11x + 2, x < 2

A:

Q: Find the first and second derivatives of f(x). f(x) = 3x – 4x + 2 f'(x) = 2 9x – 4 f''(x)

A: Recall: dxndx =nxn-1.

Q: Find the anti-derivative F(x) of the function f(x) = 2x - 7 with F(2)=55- %3D

A: We have to find the anti derivative of the given function following the given condition. anti…

Q: Find the derivative of the function. g(x) = x" + 4x° – 5x-9 gʻ(x) = D %3D

A:

Q: Find the derivative of the function. f(x) = (3x + 2)3(x2 + x)2

A: Differentiation use product formula

Q: How must f(0) be determined so that the function f(x) = x2-x ニー x0, is continuous x-1 at X= 0?

A: Let f be a real function . Let a be any point in its domain . If limx→afx exist and equal to fa Then…

Q: Find the derivative of f (x) = (x° – 4x (2² + - 8z – 2). %3D f' (z) =

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

Q: Show that the function f(x) = exp(-|x|) is not differentiable at x = 0.

A: Given function is  fx=e-x given point is x=0.

Q: : Find the value of k that makes function continuous at x = 4 %3D 3x + 6 x > 4 f(x) = 6x – k x < 4 -

A: To find: The value of k

Q: Find the second derivative of the function. . f(x) = 4x3/2 : 1. g(x) = %3D X-1 .. h(x) = secx

A:

Q: Find the derivative of the function. f(x)% 3D(x²+1)(x² + 10)/3 f'(x)%3D

A: Given equation

Q: Find the first and second derivative of the function. f(x) = 4x – 5x/10 f '(x) %3D f "(x) =

A: Given : f(x) = 4x - 5x9/10

Q: Find the second derivative of f(x)=x(x^2+1)^3

A: Find the derivative of function:

Q: Find the derivative of the algebraic function. f(x) = (4 − 3x − x2)/(x2 − 1)

A: We have to find the derivative of the algebraic function: fx=4-3x-x2x2-1 Rewriting the function,…

Q: Differentiate. f(x) = 5x^5 - 8cos(x) f'(x) = ?

A: Given f(x)=5x5-8cos(x)

Q: Find the derivative of the function. (x + 1)(2x – 5) f(x) %3D 2x + 3

A:

Q: sketch the curve f(x)= ln((x^2-4)/(x^2-3x-4))

A: given curve is                                                     f(x)=lnx2-4x2-3x-4 we have to…

Q: The critical points for the 4 function f(x) = x + – is:

A: Given,          The function is fx=x+4x .

Q: Find f'(x). f(x) = e – x³ arctan(x) -(3 + 3x2 arctan(x) + arctan(x)(3x4)) x2 +1 f'(x)

A:

Q: Find the first and second derivatives of f(x). f(x) = – 3x³ – 7x + 2 f' (x) = f''(x) =

A:

Q: find the derivative of the function:   f(x) = det [ -1  -4  3  -4  -3 ]                  [  3   0…

A: To Determine: find the derivative of the function that is f'(x) Given we have a determinate…

Q: Suppose the first derivative of a function is f'(x) = (x- 30)(19x+ 1). The function f is decreasing…

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Q: Find the derivative of f(x) f(x)= (2x+1)^3(x^2+x)^2

A:

Q: Find the derivative of the function. g (x) = 4x(3x + 2)’ %3D

A: The given function is gx=4x3x+25

Q: 1. What is the average rate of change of the function f(x) = x² - 4x + 7 on the interval 1 ≤ x ≤ 3?

A: average rate fo change in an interval (a,b) =f(b)-f(a)b-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.