. Suppose (x, t), where x, t ≤ R, is a function satisfying the до 2² (1) Ət əx² Show that p(x, t) := 4e¯ (3,−1), where x ≤ R and t > 0, also satisfies equation (1). (differential) equation -

Q: Find all local maximum and minimum points of y = 2 + 3x − x³ by the second derivative test.

A: y = 2 + 3x - x3    => y' = dy/dx = 3 - 3x2 = 0 (set)                => 3(1 - x2) = 0…

Q: Which of the following is not true for the differential operators A, B, and C? A (A+B) +C = A+ (B+C)…

A: Differential operator

Q: 4. Determine the directional derivative of f(r, y, z) = xe"+rsinz+a²y at the point (2,0, ) in the…

A:

Q: The curve y = f(x) has a y – intercept of 3. The tangent to this curve at the point (x, y) has an x…

A: Based on x and y intercept value we will find out equation of the graph.

Q: (4-х, XS0 10) Determine if the function y(X) = 3x, is differentiable at x =0. x>0

A:

Q: find the first and the second derivative of these equation , first as a function of z then as a…

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

Q: af Suppose f = f(x, y) and let |(0,5)= 2 and |(0,5) = 8. 3x Define the function g(t) = f(tº - t,…

A:

Q: The equations zy? + 8xzcos(u) + ye" = 16 and r*yz+xe" – 5u²v² = 15 are solved for u and v as…

A:

Q: Find the derivative of the function. 8) q =V10r - 15 -5r4 A) - V10r -15 B) 2/10r - 15 C)- 2/10 - 514…

A:

Q: Q4: Find the derivative of the function at P, in the direction of A 2 1) f(x, y) = 2xy-3y², P.…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: Find the derivative of the function at P, in the direction of A. 0. fxy,2) 3D ху + yz +zx, Pо(3, -…

A:

Q: A cylindrical vessel without lid is 4 cm in radius and 10 cm in height. If the vessel is to be…

A:

Q: Find the derivative of the function f (, y, z) = 4ay z at the point (4, 64, 16) in the direction of…

A:

Q: Find the derivative of the function at P, in the direction of A. f(x,y) — - Зху + 4y*, Po(-6, - 5),…

A:

Q: Solve the D. E. to the I. V. P. sinx(e-y + 1)x' – cosx = 1, y(0) = 0 %3D %3D (1 – e') (1 + cos.x) =…

A: We will find out the required solution.

Q: Let f(x) = e»in(²)+z² _ i) Find the x-values of the stationary points to the curve y = f(x), where 0…

A: The given function is  fx=esinx2+x2

Q: Q/ show that f(Z) = |Z|2= x² + y² has a derivative only at the origin

A:

Q: Determine coefficients a and b such that p(x)=x^2+ax+b satisfies p(1)=6 and p′(1)=0

A: Since you have posted multiple question in this question which are nt interlinked so i have solved…

Q: Exercise 6: Suppose f and g are functions such that: -3 f = 1, i=7, f = 5, -3 Г» g = 6, g = 3, :-4.…

A: Suppose f and g are functions such that

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 1-x (x+ 3)5 15) у - In 6х- 8 A)…

A: Given that:y=ln1-xx+35To find derivative

Q: Prob3: Find the derivative of the function at P, in the direction of A f(x,y,z) = (1.0.). = cos xy +…

A:

Q: 36. Find the critical points using second derivative test of the equation y = 2x³ + 9x² + 27 %3D a.…

A: This question is related to derivatives.

Q: Find y as a function of x if y(0) = 13, y' (0) = 22, y" (0) = 27. y(x) = y" - 15y" +56y' = 42e*,

A:

Q: Let z be a differentiable function of x and y related by the following equation: x+z (√y + cosh(z))…

A:

Q: In calculus, the derivative of f (x) is denoted by f '(x), andthe value of the derivative at x = a…

A:

Q: 2. What is the equation of the tangent line to the curve y = x? - 2x +1 at point (3,4)? а. у3 2x — 2…

A: The equation of line is y-y1=mx-x1, where m is the slope of the curve.

Q: The equations ry² + 8xzcos(u) + ye® = 16 and x³yz + xe" – 5u²v² = 15 are solved for u and v as…

A:

Q: Mrs. Wigen conducted a survey in her math class. She asked each of her students to tell her how many…

A: The data plotting helps to visualize the relationship between variables. A dot plot consists data,…

Q: 1. Determine whether the given functions are differentiable (anywhere). If the function is…

A: We will check where given function is differentiable and then we will find the derivative of…

Q: 1. Find the directional derivative of the scalar function f = yzx^2 + 4xz^2 at the point P(1,-2,-1)…

A:

Q: //welro) Find a local linear approximation for the function 5х + 6 f(x) valid for x near 5 5x + 6…

A:

Q: b The curve with equation y = ax + passes through the point (2,0) - x2 where its gradient is found…

A: