Suppose (-8, 6) is a critical point of a function f with continuous second derivatives. If fra (-8, 6) = 9, fry (-8, 6) = 9 and fyy (-8, 6) = -1, use the Second Derivatives Test to classify the point (-8, 6).

Q: Let f and g be functions of x, where a is an unknown constant. What is a valid expression for (-)'…

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Q: Evaluate W(3,-1) for the function W(x,y) = 4x^2 + y^2

A: W(x,y) = 4x2 + y2Find W(3,-1)

Q: Let f and g be functions such that f(0) = 18, f '(0) = 3, f(18) = 11, f '(18) = - 5 and g(11) = -…

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Q: 16. The derivative of the function f(x)= x - X +2 is X - 1 (x* - 2) V a) b) (x? -2) Vx x? - 2 d) X +…

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Q: Screen Shot 2021-10-05 at 9.01.21 AM.png y = (3 Vx – x2 + 2)x5 33 x9/2 – 7x6 + 10x* 2 - 33 x7/2 –…

A: See the details solution in below

Q: The curve defined by the function f(x) = ax^3 + bx^2 + 29x - 20 intersects the x-axis at three…

A: The curve defined by the function f(x) = ax^3 + bx^2 + 29x - 20 intersects the x-axis at three…

Q: • Find f" (3) for f (æ) = x³ – 2x4 + æ³ + 2x? – 7x + 3. showing the steps in your process. - -

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Q: Differentiation. Find the value of the derivative of (iz³ + 15z²)³ 3 at 10i. [(iz³+152²)³] -405000…

A: The given problem is to find the value of the derivative of the given complex function at z=10i by…

Q: Consider the interval [-2, -1].  According to the Intermediate Value Thereom, which of the following…

A: Intermediate Value Theorem:- If a function f(x) is continuous on the interval (a,b) and have value…

Q: Q3/ find the derivative D f(x) = x log5 @f(x) = (x+3) ² 2x+4 2 X

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Q: xy Find all second order derivatives for r(x,y)= 4x +9y

A: The given function is

Q: If f'(x) = x(x- 2)(x+1), then the graph of f has points of inflec- tion when x = A. -2 and 1 B. 2…

A: f''(x)= x(x-2)(x+1)2  To find the points of inflection of function f  A. -2 and 1 B. 2 and -1 C. 2…

Q: Use the deffinition of derivatives to deffrintiate y= -x3+3x-6

A: Here the given function is

Q: Find y' if 3x2- (xy²) = 2y³ 2 3=

A: Given: 3x2-xy212=2y3   As we know that; The sum/difference rule: f±g'=f'±g' The Power law;…

Q: Suppose f(x)=x^4+3x+1 on the interval [−4,−1]. Find x when f′(x)=0.

A: Given function is Differentiating with respect to x , we get

Q: f (x) = x2³ (1– x) 2/3

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Q: 1. Assume that the function f is a one-to-one function. (a) If f(2) = 5, find f-(5). Your answer is…

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Q: If point P (4,-3) is on f(x) and if g(x-2) = -3f(1-x) -5 , then determine the point P' on g(x).

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Q: 4 – x2 3 – Vx2 +5

A: We need to find the 1st, 2nd, and 3rd derivative of the above expression.   4-x23-x2+5'…

Q: Let f (x) = 5x4 + 3x3 + 3x2 + 5x + 5. Fill in the missing coefficients for the derivative of f:

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Q: Find the point on the curve g(x) = x² – 2 that is closest to the point (3,-2)

A: We can represent all the points on the curveg(x) = x2-2 as (x, x2-2)Now we will use the distance…