Let f be a differentiable function. We are given the following values of ƒ and x |ƒ(x)|ƒ'(x) 4 16 36 Consider the functions g, h, k defined by Find the following values: a) g'(4) = b) h' (4) = c) k'(4) = g(x) h(x) = k(x) = 36 2 3 7 -3 4 f(x²) fof(x) 3(f(x))³ — 1(f(x))²

Q: Differentiate the function. P'(W) = P(w) = 6w² - 4w+2 √w W

A: To differentiate the following function.

Q: -6 +3 -x+6 if x ≤ - 5 if -5 < x < 5 if x ≥ 5

A:

Q: Verify that fxy = fyx for the following function. f(x,y) = 10 cos xy fxy = fyx =

A:

Q: Find any relative extrema of the function. List each extremum along with the x-value at which it…

A:

Q: Function 9 is an even function. The right half of the function is shown on the co- ordinate grid.…

A:

Q: 27. y = x²(1 - In x²)

A: To find the derivative of the following function.

Q: A farmer plans to enclose a rectangular pasture adjacent to a river (see figure). The pasture must…

A:

Q: Find dy/dx by implicit differentiation. x²y² + x sin(y) = 6

A:

Q: The position of an object moving along a straight line for t20 is given by 5₁ = t³+8, and the…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 2 cm2/min, find the rate (in…

A: Area (A) decreases at a rateDiameter, D=8 cm

Q: A 5 m ladder leans against a wall. The bottom of the ladder is 1.3 m from the wall at time t = 0 sec…

A:

Q: Find the derivative of the function. y' = y = √√√1-x² - x cos-¹(x)

A: we need to find out the derivative of the given function."Note that as per the rules, we are…

Q: Given the following functions: f(u) =tan(u) and g(x) = x³. Find: f(g(x)) = f'(u) = f'(g(x)) g'(x) =…

A:

Q: Use differentials to approximate the value of the expression. Compare your answer with that of a…

A: By using differentials to approximate the value of the following expression.To compare the answer…

Q: v² dv (1 — v²) 5/²

A:

Q: Find the differential of the function f(x, y) = 2xe" at the point (2,4) using Ax = 0.2 and Ay= 0.15.…

A:

Q: 2. Use substitution to factor 3(x-1)² - 4(x-1)-7.

A:

Q: Kindly provide, using the graph: a.) domain and range in interval notation. b.) the interval for…

A:

Q: converging on a single point as they fly at right angles to each other. One plane is 304 miles away…

A: Air traffic control detects two airplanes at the same altitude converging on a single point as they…

Q: Consider the functions f (x) = √√ and g(x) = x - 10. a. Find (f + g) (x) and determine its domain.…

A: Given,

Q: Calculate f¹ (2) for f(x) = x³ - 2x using the difference formula: f(a+h)-f(a) f' (a) limo h Show…

A: Given, .we know,

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A: .

Q: Given the function f, find the slope of the line tangent to the graph of f1 at the specified point…

A:

Q: by defintion the Laplace transform of a function f(t) is an improper integral of the form F(s) = √°*…

A: The definition of Laplace transform f(t) Given function

Q: is the correct form of the partial fraction decomposition of -? + Dx + E x²-x+3

A:

Q: Evaluate the following limit by direct substitution. Enter the exact answer. Lim (2x² - 1) x→5 =…

A: Limx-5-1)

Q: Find dx (In √æ²+1).

A: Given that expression we have to find evaluate the value

Q: Solve the following exponential equation. Use logarithms to express the solution in its exact form.…

A:

Q: Find the first and second derivatives of the function. y = e²xsin(5x) 5e²xcos (5x) + 2 sin (5x) e²x…

A: given

Q: Thank you! I take it there is no way to rewrite this in standard form (dy/dx + P(x)y = Q(x))? Also,…

A: To write an equivalent first order differential equation, as well as an initialcondition for y.Note:…

Q: Evaluate the limit along the stated paths, or type "DNE" if the limit Does Not Exist: xy+y³ lim…

A:

Q: A 5-m ladder leans against a wall. Assume the bottom slides away from the wall at a rate of 0.5 m/s.…

A:

Q: Biologists stocked a lake with 80 fish and estimated the carrying capacity (the maximal population…

A:

Q: A baseball diamond is a square of side 90 ft. A baseball player runs from a home plate toward the…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: Winter Fun will supply a Blazing Blue snowmobiles at price p in dollars for each Blazing Blue…

A: Given

Q: Find the dimensions of the rectangular garden of greatest area that can be fenced off (all four…

A: The perimeter of a rectangle is  where  is the length and  is width.The perimeter equals 1700…

Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = 5xy - 4x² -…

A: We are given a function and we need to find out the relative maximum, minimum or saddle points if…

Q: = x - 8.

A:

Q: Let A be a 3 x 4 matrix with reduced row echelon form given by [10 5 1 3 --- U = 0 1 1 1 If a₁ find…

A:

Q: Use the properties of logarithms to expand the following expression as much as possible. Simplify…

A:

Q: For time 0 ≤ ≤ 10, a particle moves along the x-axis with position given by x(t) = t³-77² +8t+5 What…

A:

Q: cation in spherical at is equivalent to the ation x² + y²-22²=0 ya

A:

Q: Σ n = 1 n- Evaluate the following integral. [*x-7 dx Since the integral| ---Select--- Need Help?…

A:

Q: point at which the line f(x) = -5x - 16 interse

A:

Q: Find the four second partial derivatives of f(x, y) = 7x+4y7 +6x6y5. 224 2

A:

Q: Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve…

A: Note:-As per your demand we solve only part a for you The given surface equation is

Q: Use logarithmic differentiation to find the derivative of the function. 3x y=(√x)³

A:

Q: Let G=7f-g, where the graphs of f and g are shown in the figure to the right. Find the following…

A: G=7f-g

Q: Intervals of Increase and Decrease and Local Extrema Answer the following questions using the…

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: Let F(x) = f(f(x)) and G(x) = (F(x))² and suppose that Find F'(3) and G'(3). F'(3) G'(3) = = f(3) =…

A: Given,  F(x)=f(f(x)) and .Given, f(3)=9, f(9)=3, f'(9)=4, f'(3)=15