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A curve is such that =-4x. The curve has a maximum point at (2, 12). (i)...
A point moves along the curve y = VX in such a way that the y-component...
A point moves along the curve y = VX in such a way that the y-component of the position of the point is increasing at a rate of 3 units per second. At what rate is the x-component changing for each of the following values? (a) = dx dt (b) x 1 dx (c) = 9 dx de
A particle moves along the curve below. y = sqrt15 + x3 As it reaches the...
A particle moves along the curve below. y = sqrt15 + x3 As it reaches the point (1, 4), the y-coordinate is increasing at a rate of 4 cm/s. How fast is the x-coordinate of the point changing at that instant?
Problem 1. [12 points; 4, 4, 4- Consider the function f(x,y) 1 2- (y-1)2 (i) Draw the level curve through the point P(1...
Problem 1. [12 points; 4, 4, 4- Consider the function f(x,y) 1 2- (y-1)2 (i) Draw the level curve through the point P(1, 2). Find the gradient of f at the point P and draw the gradient vector on the level curve (ii) Draw the graph of f showing the level curve in (i) on the graph (iii) Explain why the function f admits a global minimum over the rectangle 0 x 2, y 1. Determine the minimum value and...
Find the equation of the line that is tangent to the curve y = 4x cos x at the point (π,-4π)
Find the equation of the line that is tangent to the curve y = 4x cos x at the point (π,-4π) The equation of this tangent line can be written in the form y = mx + b where m = _______ and b = _______
Please help on my elementary calculus hw :) - Stephany 2. A commodity has a demand...
Please help on my elementary calculus hw :) - Stephany
2. A commodity has a demand function modeled by p = 1700 -0.016x, and a total cost function modeled by C = 715,000 + 240x. (a) Find the profit and marginal profit at 2 = 700 units. (b) What price yields the maximum profit. (c) Use differentials to approximate the change in profit as the number of units sold changes from 500 units to 525 units. 3. Use implicit differentiation...
y 1/(1-x) 5. The point P(2,-1) lies on the curve C If Q is the point...
y 1/(1-x) 5. The point P(2,-1) lies on the curve C If Q is the point (x,1/(1-x), use your calculator to find the slope of the secant line PQ a. (correct to six decimal places) for the following values of x: 1.5 (ii) 1.9 (i) 1.99 (iv) 1.999 (v) 2.5 (vi) 2.1 (vii) 2.01 (vii) 2.001 Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(2,-1) i. b. Using...
A curve is traced by a point P(x,y) which moves such that its distance from the point A(-1,1) is three times the distance from the point B(2,-1)
A curve is traced by a point P(x,y) which moves such that its distance from the point A(-1,1) is three times the distance from the point B(2,-1). Find the equation of the curve and identity.
Q2(a) Find the following derivative of function f(x,y) 0 at point (2, 3). (i) dr dy...
Q2(a) Find the following derivative of function f(x,y) 0 at point (2, 3). (i) dr dy (2 marks) (ii) dr dx (2 marks) (iii) dxdy (4 marks) (b) Suppose that the volume of water in a tank for time range 0 st 56 is given by function 20) = 10 +51 - (i) Describe, is the volume of water increasing or decreasing at : = 0? (2 marks) (1) Describe, is the volume of water increasing or decreasing at =...
A curve passes through the point (0,6) and has the property that the slope of the...
A curve passes through the point (0,6) and has the property that the slope of the curve at every point P is three times the y-coordinate of P. What is the equation of the curve? Show your work in the PDF version of the test.
The slope S'(x) at each point (x, y) on a curve y = S(x) is given...
The slope S'(x) at each point (x, y) on a curve y = S(x) is given along with a particular point (a, b) on the curve. Use this information to find S (x). 2) f'(x) - 9x2 + 8x + 4; (0, 3) 2) A) (x) 2x+ B) f(x) = 3x3 + 4x2 + 4x - 3 of(x) = 9x3 + 8x2 + 4x + 3 D)/(x) = 3x + 4x2 + 4x + 3
A point moves along the curve y = VX in such a way that the y-component of the position of the point is increasing at a rate of 3 units per second. At what rate is the x-component changing for each of the following values? (a) = dx dt (b) x 1 dx (c) = 9 dx de
Problem 1. [12 points; 4, 4, 4- Consider the function f(x,y) 1 2- (y-1)2 (i) Draw the level curve through the point P(1, 2). Find the gradient of f at the point P and draw the gradient vector on the level curve (ii) Draw the graph of f showing the level curve in (i) on the graph (iii) Explain why the function f admits a global minimum over the rectangle 0 x 2, y 1. Determine the minimum value and...
Please help on my elementary calculus hw :) - Stephany
2. A commodity has a demand function modeled by p = 1700 -0.016x, and a total cost function modeled by C = 715,000 + 240x. (a) Find the profit and marginal profit at 2 = 700 units. (b) What price yields the maximum profit. (c) Use differentials to approximate the change in profit as the number of units sold changes from 500 units to 525 units. 3. Use implicit differentiation...
y 1/(1-x) 5. The point P(2,-1) lies on the curve C If Q is the point (x,1/(1-x), use your calculator to find the slope of the secant line PQ a. (correct to six decimal places) for the following values of x: 1.5 (ii) 1.9 (i) 1.99 (iv) 1.999 (v) 2.5 (vi) 2.1 (vii) 2.01 (vii) 2.001 Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(2,-1) i. b. Using...
Q2(a) Find the following derivative of function f(x,y) 0 at point (2, 3). (i) dr dy (2 marks) (ii) dr dx (2 marks) (iii) dxdy (4 marks) (b) Suppose that the volume of water in a tank for time range 0 st 56 is given by function 20) = 10 +51 - (i) Describe, is the volume of water increasing or decreasing at : = 0? (2 marks) (1) Describe, is the volume of water increasing or decreasing at =...
A curve passes through the point (0,6) and has the property that the slope of the curve at every point P is three times the y-coordinate of P. What is the equation of the curve? Show your work in the PDF version of the test.
The slope S'(x) at each point (x, y) on a curve y = S(x) is given along with a particular point (a, b) on the curve. Use this information to find S (x). 2) f'(x) - 9x2 + 8x + 4; (0, 3) 2) A) (x) 2x+ B) f(x) = 3x3 + 4x2 + 4x - 3 of(x) = 9x3 + 8x2 + 4x + 3 D)/(x) = 3x + 4x2 + 4x + 3
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