Suppose f(x, y)= g(x)h(y), where g and h are continuously differentiable functions of one variable with g(1) = 3, g'(1) =2, h(2) = 5, and h'(2) = -1. Use linearization to approximate ƒ(1.1, 2.2).

Q: Estimate f(4.03) for f(x) as in Figure 8. y= f(x), (10, 4) Tangent line (4, 2) FIGURE 8

A:

Q: Find y as a real-valued function of tif y(5) 9, y'(5) = 9. = y = 49y" 140y + 100y = 0, -

A:

Q: f (x) = a?2 + bx + c  mtan =f’= 2ax + b   At what value(s) of x is the line tangent to the graph of…

A:

Q: Find all points (x,y) on the graph of f(x) = 2x3 + 1 with tangent lines perpendicular to the line y=…

A:

Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: Find y as a function of a if y(1) = 8, y'(1) = 6. y = x²y" + 3xy' - 35y = 0,

A:

Q: Find the direction derivative of f(x.y,z)-xy'z at the point p(3.2,1)in the direction towards…

A: given function, f(x,y,z) = xy2z3 first we need to find the gradient(∇f) of this function at point…

Q: Find y as a function of a if y(1)9, y'(1) = -5. y = x²y" - 15xy' + 64y = x²,

A:

Q: 3. Find the derivative of y with respect to x in the following functions : 18x'y (ans.: (3x-2) a)…

A:

Q: What is the value of the first order derivative of the closed function given as…

A:

Q: Find y as a function of a if y(0) = -2, (0) = 9, '(0) = -62. y(x) = y" - 4y" -y + 4y = 0,

A: Given that y''' -4y'' - y' + 4y = 0 ,   y(0) = - 2 y(0) = 9 '(0) = -62.

Q: 4) Determine the equation of the tangent line to the function 2 f(x) = x at the point (3, 9).

A:

Q: Suppose the slope of the curve y = f¯¹ (x) at the point (4,7) is . Find ƒ'(7). [B] 4 [A] 1 [C] 5 [D]…

A:

Q: Find f(x) if f(2) = 3 and the tangent line at x has slope (x - 1)e - 2x, - 2x 3 fx) 2

A: