Consider the function f(x)=5x+6x^2 over the interval [0,1].

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: Use Second Derivative Test to find the location of all local extrema for f(x) = 2x³ + 15x² + 24x – 3

A: We Know that The second derivative may be used to determine local extrema of a function under…

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

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

Q: Consider the function f(x) whose second derivative is f”(x)=5x+2sin(x). If f(0)=4 and f’(0)=4, what…

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Q: Use second derivative test, If f(x) = 25x + 10 then f(x) has a 3 local maximum at the point_

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Q: Vx + 2 Determine where f(x) = is continuous. In(3x – 5)

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Q: (4-х, XS0 10) Determine if the function y(X) = 3x, is differentiable at x =0. x>0

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Q: Find all relative extrema of the function f(x) = x* – 4x2 + 2 by using the Second Derivative Test…

A: Given, The function  fx=x4-4x2+2 We have to find the all relative extrema of the function using the…

Q: By using the second derivative test for functions of two variables, find three positive numbers…

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Q: verify mean value theorem for the function f(x)=4x3 over ihe interval [0,2 ]?

A: verify mean value theorem for the function f(x)=4x3 over ihe interval [0,2 ]

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

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

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Q: Differentiate the function. 3. %3D In(x)

A: Given y=3ln(x)differeniatey'=ddx3lnxy'=3ddx1lnxApply exponent rule:  1a=a-1y'=3ddxln-1xApply chain…

Q: Compute the derivative. f(x) = (2x 4 - 4x- 1) secx

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Q: what is the differentiate of f(x)=ln x

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Q: Find the derivative of the function. y=x5 7 3x7 O y'=- 2x3.7 O Y'33 O Y'=. 2x3.7 O Y'=. 3x7 + 5x4…

A: Given, y=x5x3+7

Q: Apply the first derivative test to indentify all relative extrema. f(x) = cos² (2x)

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Q: 7. Differentiate the function using quotient rule. хех y = x + ex

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Q: Differentiate the function y=sinx2+3x3.

A: Given: y=sinx2+3x3 we know that ddxsinx=cosxddxxn=nxn-1

Q: Use the second derivative to find the location of all local extrema for f (x) = x + x2 – x3, -

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Q: Determine the relative extrema of the function f (x) = = x' 3x² 24x + 32 using the second derivative…

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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: Consider the function f(x) whose second derivative is f''(x)=4x+3sin(x)   If f(0)=3  and f'(0)=2…

A: detailed solution with explanation is given below

Q: Use secant method to estimate a root for function f(x)= x3 + 2.7x+ 2.6 = 0, starting for interval…

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Q: Analyze the stationary points of f(x) = x2ex by applying the second-order derivative test.

A: Stationary points are occurred where the first derivative of the function becomes zero. If the Value…

Q: Differentiate by using implicit differentiation x2y+xy2=6

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Q: Use Second Derivative Test to find the location of all local extrema for f(x)=2x³+21x²+36x-1

A: Local extrema.

Q: Find the derivative and simplify exy -x² = 4Y² %3D

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Q: Find the global maximum and global minimum of the function f(x)=sinx−x in the interval [−π,π].

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Q: Estimate the derivative of the function f (x) = -3 at the point a = 3. %3D

A: Here given as fx=x3-3 Differentiate with respect to x f'x=ddxx3-3=ddxx3-ddx3=13

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

A: A detailed solution is given below.

Q: Differentiate the function (x + y)1/2 = x4 + y4 by implicit differentiation.

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Q: Find the derivative of f(x) = 9 sinh-' (x²) – 9 In ( Vx4 + 1). %3D

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Q: Use Secant Method to calculate the root of a function f(x) = e-*(3.2sinx – 0.5cosx) on the interval…

A: To use decant method to calculate the root of a function

Q: Find the derivative of f(x)  =(a + 2x2) (x - x2) in twoways: by using the Product Rule and by…

A: We have given function  fx=a+2x2x-x2 At first we  will use product rule:…

Q: Find the derivative of f(x)=(sinxcosx)1/2

A: Given the function,

Q: Find y" by implicit differentiation. 5x3 + 4y3 = 9 У" - %3D

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Q: Consider the function f(x) whose second derivative is f''(x)=2x+3sin(x). If f(0)=2 and f'(0)=4, what…

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

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Q: Use Second Derivative Test to find the location of all local extrema for f(x) = 2x3+21x²+ 36x-1

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Q: Determine the local extrema for t(x) = -3x3 - N2 - 90x +1 using the First Derivative Test. %3D

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Q: 1. Use the first derivative test to find the location of all local extrema for 3 f(x) = -x³ +x+ 18x…

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: The coordinates of the critical point according to the criterion of the first derivative of the…

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Q: Find the derivative of the function f(x) = v4-x2 by definition

A: The given function is f(x)=4-x2 The definition of the derivative is given by: If a function f(x) is…

Q: Vx + y + 1 f(x, y) ,æ In (y² – x) х — 1 -

A: Given: fx,y=x+y+1x-1,xlny2-x A function f(x,y)=Mx,y,Nx,y is said to be continuous on the points…

Q: 3. х %3D у* — 2у3 2y3

A: We can find the answer as below using delta method

Q: Differentiate the given by implicit differentiation x3 - xy + y3 =1

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Q: Does f(x) 1-V1-x² continuous on the interval [-1, 1]?

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.