Find the local extrema for f(x) = „5/3 + 8x2/3

Q: find all critical points of the function f (x) = sin^−1 x − 2x

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Q: What is the critical point of the function f (x) = cos x?

A: what is the critical point of f(x)=cos(x)? for critical point, f'(x)=0

Q: Find y" by implicit differentiation. x² + 4y² = 4

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Q: Find the derivative of the function. f(x) = (x³ + s ]Inx O a. x*(1+Inx)+5 O b. x'(1+31nx)+ 5 O c…

A: We have to check

Q: Find the differential of the function y=√x3+4x at x=2.

A: Given the function:

Q: Use the first derivative test to find the location of all local extrema in the interval for the…

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Q: Find the x-value of the extrema by using the Second Derivative Test. Justify your answer. 1 f(x) =…

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Q: Find the indicated derivative. for y = dx 1 - 2x2 x* - 2x2 + 3 dy dx II

A: on doing differentiation we get

Q: 10. S(2x – 3) dx e 2x2 - ебх

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Q: Find the length of the curve y =x2/8 − ln(x) on the interval [1, 2].

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Q: Find the relative extrema using both the first and second derivative tests. f(r) = 2x³ – 9x² + 12x.…

A: Consider: fx=2x3-9x2+12x. Critical point is the point where the derivative of the function is either…

Q: The function f(x) = 1 + x decreases to 1 as x- 0. Does f(x) dx exist?

A: Given function is f(x)=1+x-1f(x)=1+1x Given integral is evaluated as follows.…

Q: Please identify the critical point,z, where the first derivative is equal to zero for the following…

A: Critical point

Q: Find the linear approximation of f(x)=ln(x) x=1 and use it to estimate ln(1.1). L(x)= ln(1.1)=

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Q: 1. f(x) =In (ta n"x)

A: Given query is to find the first derivative of the expression.

Q: Compute the second derivative with respect to x of 3x3 + 8 y = at x = 1.

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Q: Find the derivative at the given point. f(x)= at x = 0 %3D x+1 O 1/4 O-1

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Q: Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate ln(1.33).

A: The linear approximation of f(x) at x=a is given by L(x)=f(a)+f'(a)(x−a) Given, f(x)=ln(x) at x=1.…

Q: The linear approximation at x 0 to f(x) = sin(6x) is:

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Q: 7. Find the equation of a normal to y = x³ - 3x²+x-1 at x = 3

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Q: 2. Find y' by implicit differentiation. (5) xy =1+ xy

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Q: # 5) Find the extrema points for the function f (x) = using the second derivative tes 1+x x2 %3D Fon…

A: To find the extreme points.

Q: Find the second derivative 1. y = In(x^3+1) 2. y = Arctan (e^x)

A: Given: y=lnx3+1, y=tan-1ex

Q: y = e* - cos 3x + xlog.(1+x)

A: By using some formula of derivative

Q: (a) By using the chain rule and the derivative = (xl) if x>0 (-1, if x< O' dx find - (Ix – x|)DvxE…

A: Given : ddx(x)=1 ,     if x&gt;0-1 , if x&lt;0 To find : ddx(x3-x) , where x∈(-1,1) and x≠0

Q: F(x) = "(5t - 1) dt %3D

A: We need to find the first derivative of F(x)=∫x2x(5t-1)dt. By Leibniz's integral rule,…

Q: Find the relative extrema (if any) of the function f(x) = sin 2x ; over the interval (0, π).

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

A: Formula:

Q: Find y '  by implicit differentiation  2 x 2 + x + xy =1

A: Given expression is  2x2+x+xy=1             (i) Differentiating both sides of (i) w.r.t x,…

Q: If f(x) = S dt for x 2 1, find f'(2). 1+lnt

A: Simply use the formula for the derivative of an antiderivative.

Q: Find the derivative: f(x) = cos 1 + e8x 1- e6x – ebz f'(x) =

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Q: Find the derivative of the function. *sin(x) y = Jcos(x) In(6 + 3v) g'(x) =

A: use Lebniz's Rule:   d/dx ∫[a(x),b(x)] f(t) dt =f(b(x))b' - f(a(x))a' Here, a(x) = cos(x) b(x) =…

Q: Find the linear approximation of f(x)=ln x at x=1 and use it to estimate ln(1.24). L(x)=?…

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Q: Find dy by dx when  f(x) =2x²-x+5÷3x+2

A: The derivative of a function gives the rate of change of a function when an infinitesimal change is…

Q: Find the particular antiderivative of the derivative f'(x) = 3 -+x that satisfies the condition f…

A: Follow the procedure given below.

Q: Obtain the MSE of f(x) = ex.

A: MSE = Maclaurin Series Expansion f(x)=ex formula f(x)=∑k=0∞f(k)(0)k!xk

Q: Find the linear approximation of f(x)=lnx at x=1and use it to estimate ln⁡(1.3) L(x)=? ln 1.3≈?

A: First find the linear equation at x=1  then find the approximate values

Q: Find the linearization of ƒ(x) = sqrt(1 + x) + sin x - 0.5 at x = 0

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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: Find y' by direct differentiation (with respect to x). y = (5x2 + 6x − 7) ln x   and  y = (e-x)/…

A: Solution -a.)Given function -y = 5x2+6x-7lnxDifferentiating on both sides with respext to x,dydx =…

Q: Compute the second derivative with respect to r of 3x + 8 y = at x = 1.

A:

Q: What is the derivative of y (2æ)* O (2x)^(x) (1-2 In2x) O (2x)^(x) (1-In2x) O (2x)^(x) (1+2 In2x) O…

A: Given; y=(2x)x.

Q: Find the derivative. f(x)=tanh(2 + e^3x)

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Q: 5. Find by implicit differentiation for x + y = xy. dx

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Q: Find the relative extrema of f(x) = (x − 1) cosh x − sinh x.

A: Maxima and minima: f(x)=(x-1)coshx-sinhx f'(x)=(x-1)sinhx+coshx-coshx f'(x)=(x-1)sinhx…

Q: Let f (x) = 2x* – 3x3 + 5x + 1. Find the value of df-1 at x = 1. dx

A: We have given function;