1.Use the second sufficient condition for an inflection point (the third derivative test) to find the inflection point(s) of f(x) = x5 -+ 2x [A: 3]

Q: (v) Let f(x) = /2x – 1, for r > 0. Use the definition of the derivative to compute f'(x).

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Q: A function is given as x - 6y = 5– x. Calculate the derivative of y with respect to r with two…

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Q: If the derivative of y = f(x) at x = 2 is equal to " (0 " then y = f(x) is not continuous at r = 2.…

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Q: Q1) The dervative of the function f(x)= |x+2, using the definition of derivative is 1 b)- a) x+2 x+2

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Q: Find the derivative of a function at a certain number using the formula f(x) – f(x1) x-X1 x- x1…

A: Here's the solution, please have a look at it...

Q: The derivative of f(r, y) at P(1,2) in th in the direction of-2j is -3. Then the of -i - 2j is

A: It is given that the directional derivative of f(x,y)  at P0(1,2) in the direction of (i+j) is = 22…

Q: Find the derivative of the function f(z) = (3x +1)In(4x+3) %3D and then evaluate it at x = 0. f' (0)…

A: Given : f(x)=(3x+1)ln(4x+3)

Q: Use the second derivative test to find the extreme values of the function J () = x³ – su² 24X .

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Q: Let f(x) x + 1 Use the limit definition of the derivative to find the slope of the line tangent to…

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Q: Find the derivative of the function. f(x) = In(x + V7 + x²) f '(x) =

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Q: The derivative of y= xh* is O 1) (In x)(xh*-) O 2) 2 an x)(xh*) O 3) (In x)* O 4) xhx

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Q: -10 For f(x) = 2x-3 show that f'(x) = e using the limit definition of the derivative. ind the…

A: (a) f(x)=52x-3 f'(x)=limt→xf(t)-f(x)t-x        =limt→x52t-3-52x-3t-x…

Q: In what directions is the derivative of ƒ(x, y) = (x2 - y2 )/ (x2 + y2 ) at P(1, 1) equal to zero?

A: Given, , the unit vector is , here directional derivative is given as,

Q: 1. Find the derivative function for the following using the power rule: a) f(x) = x¹² b) y = 8x³ -…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Find the critical points of the following function. f(x) = 5x? - 3x – 1 What is the derivative of…

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Q: 2. Given: y = f (x) = (2x-2 + 5x³). What is the slope (gradient) of the first derivative function at…

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Q: 4. Given f (x )=x'-12x +1. Use the second derivative test to determine the local extremum off (x).

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use the alternative form of the derivative to find the derivative at x=c (If it exists)…

A: Given function is fx=x3+3x2+9. We know that, f'x=limx→cfx-fcx-c Given c=-3 Therefore,…

Q: The derivative of f(x) with respect to x is the function f'(x) and is defined as f'(x) = lim 0…

A: To find f(x+h) replace x by x+h in f(x).

Q: Use the alternative form of the derivative to find the derivative at x = c  (if it exists). f(x) =…

A: Definition used -           Alternative form of derivative -…

Q: Find f'(a) using the definition of the derivative at a point for: f(x). 1 = √x at a = 4.

A: Find derivative using  definition of f(x)=1x at a=4

Q: A) Find an equation of the line tangent to the function of x2 + (y – x)² = 9 at x = 1. dy 3) Using…

A: A).Givenx2+(y-x)2=9(y-x)2=9-x2y-x=±9-x2y=±9-x2+x -----{1}Taking positive of equation {1}y=9-x2+xNow…

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. g(x) = 2x2…

A: Given function is gx=2x2-3x. We know that, f'x=limx→cfx-fcx-c Using the above formula of derivative,…

Q: Let f(x) = (x² + 3x)e*. Determine the value of the third derivative of f(x) for x = 0.

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Q: Find the derivative of y with respect to x. 8x y = tan 3 - 24 O A. 64x2 + 9 O B. 64x2 + 9 24 Oc.…

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Q: 3- Show that this function is differentiable for all and find its derivative (2) = f(x+ jy) = x*-…

A: The necessary and sufficient condition for a complex function f(z)=U+iV  (where U,V are the real and…

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. f(x) = x3…

A: Given: fx=x3+2x2+1 , c=-2 To determine: Derivative of given function at x=c

Q: 11. Use the limit definition to find the derivative of f(x) = x² -2 x. 12. Find an equation of the…

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Q: Suppose that the first derivative of f(x) = x² In x is approximated by the following formula f'(x) ≈…

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Q: Find the derivative of f(h(x))?  What is the slope of the tan line at x=0.  f'(x)=(3x^2)+3 h(x)=2x+1

A: Given function

Q: Find the derivative of the function. F(x) = In(4 – x®) %3D f'(x) %D

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Q: 3- Show that this function is differentiable for all and find its derivative f(2) = f(x+jy) x - 15x…

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Q: 19.What is the derivative with respect to a of f(x) = 4-32 3z+2 4x-3

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Q: Find the derivative of y with respect to x. 1. x² + 4y² = 4ay

A: Given:   To find: Derivative of y w.r.t. x:

Q: 2x f{X) = 1+ X

A: Given: f(x)=2x1+x

Q: 3 Consider the function f(x) = 2+ 1+ (x+1)? Compute the derivative f'(x) . Determine all of the…

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Q: Q1) The dervative of the function f(x)= |x+2 using the definition of derivative is

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Q: Given that f(x) = (x-2)/(x+3), find the slope of the tangent line at x = 2. %3D O a. 1/2 O b. -1/5 O…

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Q: 1. Use the definition of derivative to find f'(1) 2r2 b) f(x) = Vx

A: Derivative of the function using definition

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 17) y =x*in x -x3 A) 4x3 - x2…

A: Given, Find derivative of y=x4lnx-13x3 with respect to x

Q: Suppose h(x) =23r +1 What is the correct result of the derivative of h with respect A h'(x) =3-23x +…

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Q: 4. Given f (x) =x' -12x +1. Use the second derivative test to determine the local extremum of f (x…

A: See the attachment.

Q: 6. Use the limit definition of derivative to find f'(x) for the functions below. (a) f(x) = /4r – 1…

A: limit definition of derivative is f'(x)=limh→0f(x+h)-f(x)h

Q: Suppose =V1+ Vx. What is the correct result of the derivative of g with respect to x? A 8'(x) = 2/1+…

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Q: 2. Find the derivative of (a) f(x) = x* + 3x 2+ 4e" 4 (b) f(x) = 2 tan(x)- 2"

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 1. Find the derivative of the following by using the Theorem. a. y = In(3x3 – 6x +9) b. y = In[(2x –…

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Q: 2 Find the derivative of the following function f(x)=2x-10x -8 using the limiting process a.…

A: The function is given by f(x) = 2x2-10x - 8 To evaluate : The derivative of the function using…

Q: 2 Consider the following piecewise function: f(x) = 0 4 x²+3' Use the first principles definition…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…