2. Let f be the linear function f(x) = -5x + 7. (a) The rate of change of f is (b) The graph of f is a with slope . and y-intercept

Q: What is the equation of the curve that passes through the point (1, 3) and has a slope of 2 x+3 O 9…

A: Here we have to write the equation of the curve that passes through the point (1,3) and has a slope…

Q: The demand x is the number of items that can be sold at a price of $p. For x = p2² - 4p +600, find…

A: We can solve as follows

Q: Find the slope and equation of the line tangent to f (x) = x² – 4 at the point (3, 5).

A:

Q: Find the slope of the line normal to the curve y = x³ - 2x +1 at x = 2 -

A:

Q: Examine f(x,y) = 2x2 - 4x +xy2 - 1 for relative extrema?

A: Calculate fx, fy , fxx , fyy , fxy for f(x,y) = 2x2 - 4x +xy2 - 1 as follows. f(x,y) = 2x2-4x+xy2-…

Q: The slope of the curve f(x)= at x =1 is

A: given function :

Q: 6. If two functions f (x) and g(x) have positive slope at x = a, must the function h(x) = f (x)g(x)…

A:

Q: A) the Y-intercept increases by 30 units for each unit increase in X B) that Y decreases by 30 units…

A: Y = 10 - 30X

Q: 2. Estimate the slope of Ix) at the point: a) where x = 3 b) where x = 2 YA fx) 4 3 2 1 2 3 4 5 6 1.

A:

Q: The average rate of change of the linear function f(x) =3x +5 between any two points is_________ .

A: Given that: The linear function f(x) = 3x + 5.

Q: he idea of a large, stable middle class (defined as those with annual household incomes in 2010…

A: Given that  middle class shrank from 61% in 1971 to 51% in 2011. Since the decline in percentage is…

Q: The ABC Company has determined that the cost of producing x widgets per weeks is C = f (x)= 2000 +…

A: C=fx=2000+100x-0.1x2 To find the cost of producing 100 widgets, put x=100 in cost function. That is,…

Q: 2. Given f (x) = ax² + b. a) Calculate the secant slope for xe[0, 2]. b) Find the rate of change at…

A: we have to calculate the following

Q: Find the slope of the curve x²+y²-6x+10y÷5=0 at point (1, 0)

A:

Q: Determine slope of a curve y = x³ + 1 at x = 1

A: Given,           The slope of the curve y=x3+1  at x=1.

Q: 7. By definition find the slope of curve y = x2 – 2x – 3, at P(2, 3).

A:

Q: The number of deaths N per week has been observed to be linearly related to the average…

A: Given :          The number of deaths N per week has been observed to be linearly related to the…

Q: 2. Find an equation and sketch the graph of the level curve of the function f (x, y) = 16 – x² - y2…

A:

Q: B. Find the slope of the curve at the given point. 1. y = 4 – 3x2 at (-1, 1) 2. y = x2 – 5 at (1,…

A:

Q: ATTACHED THANKYOU

A: Given that the first term of the AP is a and common difference is d.And the AP is constructed by the…

Q: Examine the function f(x, y)= 3x-5y-24x - 40y- 5 for relative extrema and saddle points.

A:

Q: 1. What is the instantaneous slope of y = 5 at x = 5?

A:

Q: Find the slope of the line that is tangent to the 2x-3 graph of f (x) at P(3/2, 0)

A: Slope of the tangent to tthe curve y=f(x)  at point (a,b)  is given as m=f'(a)

Q: The relationship between food expenditure of 25 households (y) and their total expenditures (x) is…

A: Given: ln Y^=2.24+0.364 ln Xr2=0.886

Q: The marginal profit of a product can be modeled by DP/dx = −.06x + 8, where P is the profit of…

A: Solve the differential equation by separation of variable and use initial value to find final…

Q: Find the slope of the curve y=x^3-3 at the point ​P(-2,-11​) by finding the limiting value of the…

A: Given,y=x3-3Point P -2,-11The slope of the secant line ism=fb-fab-a

Q: The slope of the line through the distinct points (x1, yı) and (x2, Y2) can be interpreted as the…

A: To Determine: the slope of the line through the distinct points can be interpreted as the rate of…

Q: How fast does the  slope of the curve y= (x2+x+1)2 change at the point where x=2

A: First derivative of a function represents the change in function or slope of the function and second…

Q: What is the instantaneous slope of y == at z = 5?

A: for the instantaneous  slope for a function f(x) at x=a we have to find f'(x) and then put x=a in…

Q: Use differentials to approximate the change in profit corresponding to an increase in sales (or…

A:

Q: The curve has a gradient function 2x - 3 and passes through (1,-6). Find the value of x when y = 0

A: Clear solution is given.

Q: The line with the rule y = 3x + 4 intersects the curve with equation ¦(x) = x2 at the points (-1, 1)…

A: Given:- The line with the rule y = 3x + 4 intersects the curve with equation f(x) = x2 at the points…

Q: What is the slope of the secant line that intersects the graph of h(x) = 16 – z at z = l and a = 4?

A: The slope of the secant line or any other line can be defined as the rise to the run ratio which is…

Q: What is the gradient of the curve y = x^3+4x^2-6x+3   at the point where x=-2 ?

A:

Q: 3. Find the slope of the curve of the function y = at the point P (2,-).

A:

Q: The volume of a container is given by V = ar² ( h + 1) cm³ , where r(radius), h(height) are…

A:

Q: Find a formula for the linear function with slope −3 and x-intercept 2.

A: Refer to the question.For the linear function with slope −3 and x-intercept 2, use the slope…

Q: Find the slope of * y+ Vx+ y =x at (3,1)

A: A detailed solution is given below

Q: What is the output when the input is 4 for a linear function that has a y-intercept of 5 and a rate…

A: Given information: The input of the linear function is 4. The y-intercept of 5 and the rate of…

Q: The gradient of the tangent to the curve y=-3x³ + 4ax² - 5x + 4 at x = 1 is 2. The value of a is 2.…

A:

Q: Find the points on the graph of x5/2 + y5/2= 1 where the slope of the tangent line is -1.

A: Topic:- application of derivatives

Q: 3.Find the coordinates of the points on the curves y =x3 -3x2-12x+10 with the gradients -2.

A:

Q: Find the gradient of the curve . Y=4x^2 at x=3

A:

Q: the point (-2, 0). Find the minimum rate of change of f(x, y) = x²e-2y at

A: Given: A function f(x, y)=x2e-2y and a point (-2, 0). To find: The minimum rate of change of a given…

Q: The idea of a large, stable middle class (defined as those with annual household incomes in 2010…

A:

Q: The slope of the line through the distinct points (x1, y1) and (x2, y2) can be interpreted as the…

A: The slope of the line through the distinct points (x1, y1) and (x2, y2) is defined as…

Q: y is a linear function of x with slope −4. If y is −3 when x is −1, what is y when x is 8? You do…

A: Linear Function  Y= mX+c  m= slope of function  c = Y intercept

Q: 1) Find the slope of the line tangent to the graph of y=x²+1at(2, 5).

A:

Q: 2. Estimate the slope of ffx) at the point: a) where x = 3 b) where x = 2 f(x) 4 2 1 2 3 4 5 6 3. 1.

A:

Exponential Growth Model

The relation that represents an exponential function is: