Find the absolute maximum and absolute minimum of f(x)=e^(−2x) over the interval [−1,3].

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

A: We have to find derivative of the function using limit process: fx=x+4 We know the formula of…

Q: Find the critical numbers of the function and apply the First Derivative Test to identify all…

A:

Q: Evaluate the second derivative at this critical number.

A:

Q: Find the number x in the interval-;,1| so that the difference of the number from thrice'its cube is…

A: How to find point where the function f(x)  is minimum: find f'(x) and solve f'(x) = 0 for x. after…

Q: According to the criterion of the first derivative, the image function has a point: f(x) = x2 + 10x…

A: The given function f(x)=x2+10x+21

Q: Differentiate the function. y = etan(θ)

A: Given y=etanθ Use chain rule of differentiation to differentiate the given function.

Q: Explain how the First Derivative Test determines whetherƒ(x) = x2 has a local maximum or local…

A: Given:   f(x) = x2 To determine whether f(x) has a local maximum or local minimum at the critical…

Q: Find the derivative of the function by the limit process. f(x) = 6/x

A: Given fx=6xddxfx=limh→0fx+h-fxh

Q: 3. Why first derivative is zero at local maximum and local minimum of function in an open interval?

A: Given, Why the first derivative is zero at the local maximum and a local minimum of function in an…

Q: at the point (2, –1). Find the maximum rate of change of f(x,y): x2 + Y

A: For maximum rate of change we need to calculate magnitude of gradient bat point (2,-1)

Q: Find the derivative of the function by the limit process. f(x) = √(x + 4)

A: Given function is

Q: Find the derivative of the function: f(x) = ln X x+1* Is there a shortest way? Please explain.

A: We can find the answer in the following steps.

Q: 2.) Investigate the derivate of the function ƒ(2)=Imz by using definiton of derivative.

A:

Q: What are the maximum and minimum values in application of derivatives?

A: We have to define the maximum and minimum values in application of derivatives.

Q: Find two positive numbers with product 289 and whose sum is a minimum.   Enter your answers in…

A:

Q: y=9 arctan (x+sqrt(1+x^2) )

A: ddx(xn)=nxn-1 ddxx =12x ddxtan-1(x)=1x2+1 Chain Rule: if f=f(u) where u is a function of x then…

Q: The second derivative test fails when f" is zero or does not exist at the critical number of the…

A: Given data: The value of the second derivative of the function is f''=0.  Suppose at the given point…

Q: Find the maximum or local minimum f(x)=sinx.[0,4]

A:

Q: Estimate the root very near x = 0.4 of 4(x*)" - 4(x²) + 1 = 0 using the Newton- Raphson Method with…

A: Consider a function:  fx=4xx4-4x2x+1      =4x4x-4x2x+1

Q: The maximum value of y = cos x for - < x< is 1

A:

Q: What is the connection of the concept of limits to slope to derivatives (delta method to simple…

A: The limits of the function at a point are calculated using the formula . The limits are used to…

Q: Find a function that has x^6 as its derivative without using integral knowlegde.

A: In this question, we need to find a function that has x6 as its derivative.

Q: find all possible functions with the givenderivative. y' = √θ - sec2 θ

A: Given: y'=dydθ=θ-sec2θ for evaluating solution of given differential equation, we use variable…

Q: Give an example of a differentiable function ƒ whose first derivative is zero at some point c even…

A:

Q: Consider a rectangular poster that contains 312.5 cm² of printing with a 10 cm margin at the top and…

A: Solution :- let the paper size be x cm in length and y cm in width  The length o the printed space…

Q: Differentiate the function. y = etan(8) y' =

A: The given function is y=etanθ.

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

A: f(x) = x2 + 4x + 5 h = Δx = 2 xi = 3         f(xi) = 26 xi+1 = 5          f(xi+1) = 50 xi-1 = 1…

Q: Derive a formula that approximates the second derivative of the function sampled at x = 0, 0.01,…

A: Let us assume that second derivative function  f"x0=Afx0+Bfx0-h+Cfx0+2h can be rewritten as…

Q: Integrate xtanx with respect to x

A: We have to solve this integral by  Integration by parts rule, Formula is  ∫uvdx=u∫vdx-∫u'∫vdxdx

Q: Determine the Derivative of the Function: 1. y = ex - 1/ex + 1 2. y = x22x 3. y = 43x^2 4. f(x)…

A: Find derivatives

Q: 2. Use an example to show how to use the First Derivative Test for critical points

A:

Q: Find the critical value of f (x) = vx² + x – x using the second derivative test. %3D

A:

Q: find any locl maximum and locl minimum values by using first derivative: f(x)-x-2x

A: Given :           f(x) = x4 - 2x2

Q: Q4/ Explain the rule of maximum and minimum using Derivatives with an еxample?

A:

Q: A piece of wire, 370 cm long, is to be bent into an isosceles triangle. What should the exact…

A: given: A piece of wire, 370 cm long, is bent into an isosceles triangle. we have to determine what…

Q: Show that the function has partial derivative at the point (0,0) but is discontinuous at this point.

A: solve the following

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: Find the linear approximation of the function f (x,y) = ln (x - 3y) at point (7,2).

A: To find the linear approximation of the function fx, y=lnx-3y at the point 7, 2.

Q: Explain how to find a first partial derivative of a function oftwo variables.

A: To get the first partial derivative of a function z = f(x, y) with respect to x we have to…

Q: Solves methad of vriation of Parameters - secx by the yot gosx +イne

A: We use the method of variation of parameters to solve this problem.

Q: Find the relative extrema using both First and Second Partial Derivative test f(x) = 1+8x - 3x2

A: i) The given function is fx=1+8x-3x2. Note that, the above polynomial function is real and defined…

Q: find any locl maximum and locl minimum values by using first derivative: f(x)=x*-2x?

A: The given function: f(x)=x4-2x2 To find the first derivative of the function: f'(x)=4x3-4x Now, let…

Q: 2. Find two positive numbers whose product is 750 and for which the sum of one and 10 times the…

A: Product of two numbers:= 750; Sum of one and 10times the other is minimum;

Q: What are the real-life applications of antidifferentiation or integrat

A: What are the real-life applications of anti-differentiation or integration?

Q: Find the critical numbers of the function and apply the First Derivative Test to identify all…

A:

Q: Find 1" and 2nd order partial derivative for the function ax²+by²+2hxy and also verify дхду дудх

A:

Q: Find all critical numbers and use the Second Derivative Test to determine all local extrema.

A:

Q: Explain whether the Quotient Rule should be used to find the partial derivative

A: Partial Differentiation:     ∂∂x(xyx2+1)ddx(uv)=v.dudx-u.dvdxv2