Determine where the function is concave upward and where it is concave downward. (Enter your answer using interval notation. If an answer does not exist, enter DNE. rx) = (x - 9)2/3 Concave upward:

Q: Determine whether the function t(xry, 2)=x' +y-2 (where Y,/ and Ź are s tritly greater than 0) is…

A: Use Hessian matrix

Q: Please

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Q: 3V5 – 10a2 + 6V f(r):

A: Given:f(x)=3x5-10x2+6x33x

Q: Find the inflection point(s), if any, of the function. (If an answer does not exist, enter DNE.)…

A: We first find f"(x) using the power rule

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A: We find dx/dt and dy/dt.

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A: To determine the critical point of the given equation.

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A: Given : The function y = 36 - x2.   To find the differential dy.

Q: Find the x-coordinate on the graph of f (x) = x ³ – 12 x where the tangent is horizontal. A) 1,-1 B)…

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Q: Differentiate the following function. y= e x6 to d y' = %3D dx Teto %3D

A: Given : y = ex6

Q: Calculate L6 for f(x) = v6x + I over [1,3]. %3D (Give your answer to three decimal places.) L6 =

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Q: Find dy/dx and d²y/dx². x = t2 + 7, y = t² + 9t dy dx2 For which values of t is the curve concave…

A: Here we have to differentiate the given parametric equation.

Q: For the function F(x) = [ 2|t|dt, find the tangent lines which are parallel to the bisector of the…

A: 1. Slope of equation is equal to dy/dx 2. Equation of line at point (a, b) and slope = m is :…

Q: Express the function in the form  f ° g

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Q: Where is f(x) = differentiable? %D

A: The objective is to check where f(x) is differentiable.

Q: If f(x) = |"(9 – t2)e dt, on what interval is f increasing? (Enter your answer using interval…

A: The function is fx=∫0x9-t2et2dt By second fundamental theorem of Calculus, f'x=9-x2ex2. Set the…

Q: Differentiate with respect to x, assuming that y is implicitly a function of x. dy (Use symbolic…

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Q: dy for the function y = dx 7) Using the first principles definition, determine 2x

A: topic - derivative of a function

Q: Q4) find at t= from the following functions, x= cost . y= 1+sint

A: Given that  x=cost  y=1+sint  To find the d^2y/dx^2 at t=π/2

Q: Differentiate the following function. 7 y =. /x +1 d 7 dx Vx +1

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Q: Does the function I(x. y) is harmonic ? Q5) Evaluate: So So x+1) dzdydx

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Q: The volume of a right-circular cone of radius r and height h isV = π/3 r2h. Suppose that r = h = 12…

A: Consider the given: Volume,V=π3r2hr=h=12 cmDifferentiate w.r.t. "r",dV=π32rdrh    ⋯⋯11cm increase in…

Q: Given the function f(x) = a?e3", Determine the open interval(s) where the function is concave up

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Q: Plot the following functions over the interval 0<x<4 in the same a) x3 plot: b) e* c) ex2

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Q: Determine the open intervals on which the graph is concave upward or concave downw enter DNE.) y =…

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Q: (x* + 2ху — 4y?)dx — (x? — 8ху — 4у?)dy %3D 0 -

A: Explanation of the answer is as follows

Q: Use the fplot command to plot the function f(t) = Vlcos(3x)+ sin (4x) in the domain -25 x S2.

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Q: Is differentiable at x = 2? Justify your answer

A: Given: fx=x2-5x+6x-2 for differentiability we first check it's continuity at x=2 so, we find limit…

Q: Find the derivative of the function f(x, y) 5x2-3y at (8,4) in the direction of A = 3 i-4j O 412 492…

A: First of all we will find gradient, then we will find the directional derivative

Q: XVI. Find the tangent to z = x²e° when x = 2, y = 0.

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Q: 2. (x? + 2ху — 4у?)dx — (x? — 8ху — 4у?)dy %3D0 -

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Q: 2x f (x,y) = Vx2- y²

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Q: dy d²y Find and dx dx² x=t² + 4, y = t² + 9t 11 dx d²y dx² For which values of t is the curve…

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Q: 4. Use the fplot command to plot the function f(t) lcos(3x)+ sin (4x) in the domain -25 x S2. %3D

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Q: Consider the function f(x) = 1/10 x^5 − 3x^3 − 7x + 9. a) On which interval(s) is f concave up? b)…

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Q: Define what it means by for y f(x) dx

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Q: 4. Given a function, fix), such that f(x)dx = 10, calculate: a) - r(«)dx b) S rx - 2)dx d) Stsx) +…

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Q: f(t) = -200 + 6 Sinh(4t)

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Q: Calculate L6 for f(x) = v7x + 2 over [1,3]. (Give your answer to three decimal places.) L6 =

A: I am going to solve the given problem by suing some simple calculus to get the required result.

Q: For f(z) =, find dy using the definition, 127

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Q: nd the point of inflection and discuss the concavity of the graph of the function. f(x) = sin , [0,…

A: Follow next step

Q: Determine the value(s) of x for which the line tangent to f(x) is horizontal. (Enter your answers as…

A: Given,

Q: Q4) find at t= from the following functions, x= cost. y= 1+sint

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Q: Q:A- Find for the following functions: - 1+x* 1- 1+secy

A: Given: xy21+secy=1+x4 For finding dydx, we simplify given expression then differentiate it

Q: Consider the function f(x) = e^x2−6x+5 . Find the value(s) of x at which the tangent line is…

A: Given thatf(x)=ex2−6x+5ddx(f(x))=ddx(ex2−6x+5)               =ex2ddx(x2) −6               =2xex2-6

Q: Find dy for the following functions (メ+リ)+(メーツ)ニxャガ 4.

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Q: End the solution and dyined the interpal at which function is depince dx

A: Given that xdydx+y=1y2Solution :xdydx+y=1y2xdydx=1y2-yxdydx=1-y3y2y21-y3dy=dxx∫y21-y3dy=∫dxxlet,…

Q: Use the figure to evaluate the following function, given that h(x) = tan x. Ay 2+y? =1 N/3

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Q: Q4) r(x,y) = x'/s – ½y? is harmonic ? Does the function %3D

A: The given function isf(x, y)=x13-19x-53y2to check the function is harmonic?

Q: Given that dy/dx = (x^2) and y=3 when x = -1, find the function f(x) in terms of x y-x+c--1 C

A: dydx=x23=x23