7, The inflection points of the function f(x)%= 글어 -금 + 12-음 ocurs at OCcurs at: ||

Q: Find the equation of the normal line of f(x) = x⁴ + 2x at x = 1 using the limits definition.

A:

Q: The mean value of c, for which f '(x) vanishes (i.e., becomes 'zero'), for f(x) =x2 - 6x + 8 in…

A: Given,           fx=x2-6x+8 in 2,4 and f'x vanishes.

Q: of f(x, y, tion of ve

A:

Q: 4. Is the function given by G(x) 1 x-1 the interval (0, ∞)? Why or why not? continuous over

A:

Q: Find (f - g)(x) if f(2) = 7x³ – 52² + 42x – 30 and g(z) = 7 O (f · g)(x) = 49zª + 269x² + 150 O (f·…

A:

Q: What is the first derivative of q(x) = In (4x² + 3x+2)? Select the correct answer below: In (8z + 3)…

A:

Q: Find the average rate of change of the function between the given values of x. y = −5x − x2 between…

A: The given function y and the values of x between which the average rate of change of y is to be…

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

A:

Q: If f(x) = etan-¹(x²-3) then f'(x) at x = 2 is equal to

A: SOLUTION-

Q: - Show that charactaristic function associatel with two distinct chavacteristic values always…

A: We have to show that the eigenfuctions/characteristic functions associated with two distinct…

Q: 2. Calculate the first derivative of f using the forward and backward difference approach in the…

A: The objective is to calculate the first derivative of f using the forward and backward difference…

Q: Identify the equation of the normal line of the funtion f(x) = -3x at x=2

A:

Q: 2) Let f(x) = x' +x² – 5x – 5. Use the second derivative test to classify the critical points.

A:

Q: (a) f(xi), f(xi+1) and f(x+2) are three data points of f(x) and equally spaced at x with the step…

A:

Q: Find the first derivative: y = In V2r³ – 5 O y =: 22-5 O y = 4z 22-5 O y = 62 22-5 O y =; 2z-5 O y =…

A: Here we have to find the first derivative of         y = ln(2x3-5)1/3

Q: X = (1-_-_-_-)* 2 o then f(x) tend:

A:

Q: Find the derivative of the function. (3x +5) f(x) = In (7x + 5)*(2x+ 8) 14 2 O a. 3x +5 + 7x +5 2x…

A: We have to check

Q: Suppose that a firm uses L as an input, and its production function changes with L and a parameter…

A: Let’s apply the above approach to an economic application, namely the profit function of a…

Q: In 5 x+1 Find the derivative of y = logs ((*)) with respect to x-1 independent variable x.

A:

Q: Locate the critical points of the function f(x) = x + 2x + 6x - 4 and use the second derivative test…

A: We solve the equation f'(x)=0 to find the critical points of the function. If a is a critical point,…

Q: The tangent line to y = f(x) at (-1,-8) passes through the point (-7,5). Compute the following a.)…

A: The tangent line to y=f(x) at (-1,-8) passes through the point (-7,5)

Q: . Determine the upper bound on the error in the approximation: x2sinx3 x. - if x|<0.8 6.

A:

Q: The first derivative of the function h is given by h' (x) = x³ – 3x2 + x. What are all intervals om…

A:

Q: [4] 2. Find f'(x) using the limit definition of the derivative. Credit will not be given for any…

A:

Q: 2. What is the average rate of change of the function f (x) = x² – 3x over the interval [1,1.01]?

A: use average rate of change formula .

Q: Find the extreme values of the function f(x)=x√√1- x .- x on the interva

A:

Q: Compute the derivatives of the given functions. f(2) = In (7z²). 7a?). f'(x): / (z) = help…

A:

Q: Suppose the derivative of ƒ is ƒ'(x) = x - 3.a. Find the critical points of ƒ.b. On what intervals…

A: We have to find: a. critical points of fb. On what intervals is f increasing and on what intervals…

Q: Find the derivativeof the following function:

A: To determine derivative of the function.

Q: Approximate the derivative of f(x)-x3+4x2-10x+5=0 at x=3 using the forward, backward and central…

A:

Q: 1. Solve the first derivative of f(x) = e-2x In x at x = 0.5 using forward finite-divided difference…

A: To find the first derivative of the function f(x) = e-2xlnx at x = 0.5 using forward finite-divided…

Q: nd the derivative by the limit process (Gener x) = Vx2 - 4

A: In this question, the concept of the derivative is applied. Derivative The derivative is used to…

Q: For a function f (x, y), (0, 0) and (1, 1) are two critical points. Also, fxx = 2x², fyy = y²2 and…

A:

Q: In(8z) Siven f(z) the derivative f'(x) is 8. %3D O 8 8x o 1 O 78z 1 8x 1/8

A:

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

A:

Q: The rate at which the total average number of COVID cases is increasing at x=10 tents and dxdt=1…

A:

Q: find a linearization at a suitably chosen integer neara at which the given function and its…

A: Consider the following function: fx=x2+2x Differentiate fx with respect to x: ddxfx=ddxx2+2xf'x=2x+2

Q: [1, 2). over Calculate M6 for f(x) = 3 · In(x³) M6

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

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

Q: The tangent line to y=f(x) at (−8,−5) passes through the point (−3,10). Compute the following f(-8)…

A:

Q: Find the first derivative: In 2x f (x) 1- In 2x f(x) = In (sec x) f(x) = cos (In x) f(x) = In[cos…

A: we can answer only three subparts, or the first question and the rest can be reposted. No more than…

Q: 4. Use the first and second derivative to find the absolute maximum and minimum, if either exists,…

A:

Q: 5, i, Evaluate the first and second derivatives of the function z=2x4+3x3+2x-5 when x = 4. ii, Find…

A: The objective of the question is evaluate area and find derivatives of given functions.

Q: 5)Let f ( x ) =3x4 + 4x3 Find the derivative. b)Find the critical numbers.

A: Given problem:- 5)Let f ( x ) =3x4 + 4x3   a) Find the derivative.   b) Find the critical numbers.

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: To determine if the function has any points of maxima, minima or inflection, use second derivative…

Q: 3 Find the derivative with gicapeet to X If f(0 = 0-7 The derivatie with reapeet to X If -7X is…

A:

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

A: Here the first derivative of the given function is y’= 6 x (x+1) (x-2). If a function has zero…

Q: In x g(x) = 2

A:

Q: 6. Use the difference quotient to estimate the 2 instantaneous rate of change in f(x) = x² at x=3…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.