For what value of x does the function g(x) - 2x? concave downward? А. x2 -1 x 2 0 С. x 2 -2 D. x< 2 B.

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: Let f (x) = x3 – 3x2 – 1, x 2 2. Find the value of df-1 at the point x = -1 = f (3). dx -

A:

Q: Find the antiderivative F(x) of f(x)=x/3(12x2-6), given F(1)=5

A: An anti derivative of a function f is a differentiable function, whose derivative should be equal to…

Q: 1+х f[X_, Y_] := 2 у - 1-x (1+) (у-1)2

A: We will use basic knowledge of the functions of several variable theory to answer this question.  We…

Q: Consider the function f(x)=x^2(e^(10x)) f(x) has two inflection values at x = C and x = D with C≤D…

A: We find the second derivative using the product rule

Q: Suppose that f: R R is a differentiable function, satisfying f(3)35 and f(x) dx=8. What is the value…

A:

Q: find the diferential of the function when x = 2 and dx = 0.1 f(x) = x ln (x^3 + 2x - 4)

A: We will use the definition of differential.

Q: -3r 10 f(x) : r2--20 C, r= 5 What value of C would make f(x) continuous at r 5?

A:

Q: For what value(s) of x is f(x) = 4?

A: The first thing we must do for this case is observed the y coordinates for a given value of x…

Q: f(x) = 2x2 - 3x + 4, Find the equation of the line which tangent to this function at x = 1 O a. y =…

A: We have to find the equation of the tangent to the given function at given point. We know that slope…

Q: Suppose that f: R→R is a differentiable function, satisfying f(4)=2 and | f(x) dæ=5. What is the 4.…

A: Integration by parts ∫uv'=uv-∫u'v

Q: Find a linear approximation to f(x) = 4xe2*-6 at x = 3. Use this linear proximation to estimate the…

A: To find Linear approximation

Q: Find, if they exist, the extrema of the function: f(x, y) = x² + 3y? + 4,

A:

Q: Find the family of antiderivatives for the function, f(x) = 8 12x. Which of these pass through the…

A: To find the family of antiderivatives for f(x) integrate f(x) with respect to x.

Q: of Find - for the following function. and 5xy f(x.y) = e In (3y)

A: Given: Now,        ∂ ∂ xe5xyln3yTreat y as a constant=ln3y∂ ∂ xe5xy=e5xy∂ ∂ x5xy=ln3ye5xy· 5y

Q: d f'(a) for the function f(x) = 3x-2. swer: f'(a) =

A:

Q: Find the antiderivative F(x) of f(x)=x(2x+7), given F(4)=5

A: Given:The function is f(x) = x(2x+7), F(4) = 5.

Q: If a F (z) = xy+ i (x² – y²), what is F(-1+ 2i)?

A: The given question  is related to complex numbers.  Given F(z)=xy=xy+i(x2-y2) We need to find…

Q: Differentiate the function In e* 8.) y = ex 7.) f(x) = e** – In :

A:

Q: For what value of the constant c is the function f continuous on (-0, 0) if x < 5 f(x) ={ cx? + 8x…

A:

Q: The antiderivative of the function f(x) 5 + 10x is

A:

Q: On what interval(s) is the function y = –2x² + 3x/3 both increasing and concave down?

A:

Q: (a) If e19z f (2) = z10 + 49 at how many points the function f (z)is discontinuous ?

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

Q: At which r-values is the following function g differentiable? Explain and compute, where necessary.…

A:

Q: For the function f(x) = 4x² + 2, the slope of the tangent line at x = 3 is a m = 32 b m = 4 m = 8 d…

A:

Q: If f is an even function, why is S", f(x) dx = 2 f“ f(x) dx?

A: A function is said to be even if f-x=fx   We have to prove  ∫-aafx dx=2∫0afx dx   Consider left hand…

Q: For function f(x,y) to have no extremum value at (a,b) is? 1) rt - s>0 2) rt – s?<0 3) rt - s? = 0…

A: To select: The condition for the function f(x, y) to have no extreme value at (a, b).

Q: of af For the function f(x.y)= 7x-9y- 3, find and dy

A:

Q: Why is ƒ not a function from R to R if f(x)= ½? b. f(x)= Jx ? c. f(x)=±/(x² +1)? а.

A: Why is f not a function from R to R if,  a) f(x)=1xb) f(x)=xc) f(x)=±x2+1

Q: Given the function, f(x) = √x + x, use linearization at x = 4, to approximate f(4.1)

A:

Q: For what value of x does the function g(x) = Ex + 2x? convex? -- x> 1- В. x< 2 C. x< 2 D. x 2 1 A.

A:

Q: For what value of x does the function g(x) =--x³ + 2x? strictly concave downward? А. x> 2 В. х>1 С.…

A: Use the property of strictly concave downward i.e.g"(x) &lt;0.

Q: Q1) Find the local extreme values of the function f(x, y) = 3y² - 2y -3 x + 6xy %3D

A:

Q: Which of the following functions is differentiable for all values of x? a. fAx) = 2r' + 5x² b.…

A: Given problem:-

Q: If f is a positive function and f"(x) < 0 for a < xs b, show that T, < f(x) dx < M,

A: f is a positive function and f''(x)&lt;0 for a≤x≤b This tells us that f is concave down over the…

Q: Q3) prove that: fa+¹h f(x).dx h 2h 4h - = 3 [ƒ (a) + f(a + 4h)] + f(a+2h) + [f(a+h) + f(a + 3h)] 3 3

A: Introduction: Numerical integration is a word utilized in evaluation to explain a set of strategies…

Q: ах + 4 when x< 2 f(x)= x? — 6х +b 2 when x22 -

A:

Q: 5. Find the antiderivative of the function and check your answer by differentiating. f(x) = 9x +…

A: 5. We need to evaluate the antiderivative of the following function fx = 9x+15x-2

Q: (b) If 38 10z f (2) = (2** + 6) e then at how many points the function f (z) is not differentiable?

A: f is every where differentiable, there are no points such that the function f(z) is not…

Q: of the functions f(t) = e² implified.

A:

Q: Suppose y is a differentiable function of r. Find y' if 2xy 3 2y3 + 5x4. y2 -

A:

Q: find the diferential of the function when x = 2 and dx = 0.1 f(x) = 3 / (x-1) ^ 2

A: Given that f(x)=3(x-1)2 Take the derivative with respect to x, dfdx=-6(x-1)3df=-6dx(x-1)3

Q: If f(1) = 13, f' is continuous, and F'(x) dx = 18, what is the value of f(6)?

A:

Q: (x) is an even function, and if f 6 f(x) dx = 15, find f³, f(x) dx.

A: Given query is to find the value of the Indicated integral.

Q: of find and of For the function f(x,y) = x+ 8y ду

A: Function given is- f(x,y)=6x+8y To find- ∂f∂x and ∂f∂y ∂f∂x=Partial derivative with respect to  x…

Q: y? For function f (x, y) x2+1 Starting from the point (1, 2), at which direction does the above…

A:

Q: y2 For function f (x, y) = x2+1

A:

Q: Suppose that f: R→R is a differentiable function, satisfying f(3)=5 and f(x) dx=8. 3 /x-s'(x) dx?…

A: