9. The graph of the quadratic function f(x)=c+bx-x intersects the y-axis at point A (0, 5) and has its vertex at point B(2,9). A (a) Write down the value of e. (b) Find the value of b. (c) Find the x-intercepts of the graph of /. (d) Write down f(x) in the form/0)=-(x-p) (x+g).

Q: Find the absolute maximum value of the function y=xV3x-x² on the interval [0, 3].

A:

Q: 7) A rectangle has its two lower corners on the x-axis and its two upper corners on the curve…

A: Follow the procedure given below.

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A: Given that: y = ax3 + bx2 + cx has a local maximum at x = 3, local minimum at x = -1, and inflection…

Q: The equation of a quartic function with x-intercepts at 1 (order 2), -3 (order 1), 2 (order 1) and…

A: Let's find.

Q: 1. A company manufactures and sells a televisions per month. If the cost and the revenue functions…

A:

Q: find the orthogonal trajectories of the family of curves x2+y2=a2

A:

Q: Find the quadratic approximation to f(x) = /x + 3 near a = 1. Graph f, the quadratic approximation,…

A: fx=x+3

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A:

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A:

Q: 3:- Find the maximum value of the function f(x, y) = x²y on the line x + y = 3.

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

Q: 104v 2 -10 -8 -6 -4 -2 0 4 6 8 10 -2 -4 -6 -8 -10 Match the graph with its function by translating…

A: topic - translation of a function

Q: 4. Determine the maximum point of the the graph of y = 12 sin(π – 2x), for x = [-T, T).

A: Given:         y=1-2sinπ-2x     To get the maximum value of the function the derivative is equal…

Q: 1. Use the first derivative test to find the local minimum and maximum points of the graph of f(x) =…

A:

Q: 3) y =x² +2x - T 4) y=x² – 8x + 14 2.5 1.5 0.5 -1 -0.5 -3 Find EXACT Vaiue's of x- intercepts For…

A:

Q: Find the slope of the curve y=x2−3x−4 at the point ​P(2​,−6​) by finding the limiting value of the…

A: Giveny= x2-3x-4 = f(x)at point ( 2, -6)as f(x) =x2-3x-yand f(2+h) = (2+h)2-3(x+h) -4…

Q: 27The platis that passes through the e Point C672) and contains the lihie メー4-2t)X= 345t) Zと+4t 4. こ

A: We have to find the equation of the plane which passes through the given point and contains the…

Q: The line tangent to y = ƒ1x2 at x = 3 is y = 4x - 10 and the line tangent to y = g1x2 at x = 5 is y…

A: The line tangent to y=fx at x=3 is y=4x-10 and the line tangent to y=gx at x=5 is y=6x-27. Consider,…

Q: Determine the values of constants a, b, c, and d so that ƒ(x) = ax3 + bx2 + cx + d has a local…

A:

Q: O Fend an equalion of the tangont line to the graph-of y-x-4Vx at (1-3). O Find an equalion -of #he…

A: If the slope of a line and any point (x1,y1) on it is known then its equation is given by :…

Q: b- find any locl maximum and locl minimum values by using first derivative: f(x)=x-2x²

A: We can use application of derivative order to solve the given problem.

Q: 1. For what value (s) of x is the function f(x) = 4/2x2 - 6x not continous?

A:

Q: 4. Find the orthogonal trajectories of the family of parabola described by the equation (y– 3) = Cx.…

A: The solution of the problem is given in the next step.

Q: N(t) components per day after t days of traning where N(t)=75t/t+5 t> or = 0. Sketch the graph of N…

A:

Q: 9. The average revenue function of x units of product is R(x)=-mx+n,where m and n are constants. a)…

A: Given that: Average revenue function, R¯(x)=-mx+n

Q: Find constants a and b so that the minimum for the parabola f (x) = x² + ax + b is at the point (4,…

A:

Q: 5 Find the point X to minimize the function f(x1, x2) =1+¤1 +2x2+ from the strating point X, = using…

A: We are given the following optimization problem : f(x1 , x2) = 1 + x1 + 2x2 + 5/x1 + 10/x2 And we…

Q: Determine the maximum number of turning points of f. 6. f(x) = (x – 2)2(x + 4)2 7. Identify the end…

A:

Q: b- find any locl maximum and locl minimum values by using first derivative: f(x)=x*-2x²

A: Points of local extremum can be calculated by using the first derivative. These are points which…

Q: (5) Find the curve y = f(x) in the xy-plane that passes through the point (9, 4) and whose slope at…

A:

Q: | 1) Find a function y whose graph passes through the point (1, ) and satisfies x²y' = y.

A:

Q: Do you agree with this statement. Cubic functions must have at least one x intercept but not more…

A: Given statement : Cubic functions must have at least one x intercept but not more than 3 whereas…

Q: Find the values of constants a, b, and c so that the graph of y = ax + bax2 + cx has a local maximum…

A:

Q: 2) Find the equation of a quadratic function with a maximum value at (2,5) and a vertical intercept…

A: We have to find equation

Q: The graph of f(x) = 2a² + 12z² – 72z + 14 has two horizontal tangents. One occurs at a negative…

A:

Q: Find the value of x at which the minimum of the function f(x) = x? Occurs.

A:

Q: 3. To achieve the maximum benefit for the heart when exercising, your heart rate (in beats per…

A:

Q: ve maximum or

A: Maxima and minima: Let f(x)=e3x2+4 For maxima or minima we need to find those values where f'(x)=0.…

Q: Determine all the critical points for the function y = Vx² (2t- 1)

A: Given function is in two variables x and t For critical points we calculate Partial derivatives…

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

A:

Q: The time (in hours) that a branch of Amalgamated Entities needs to spend to meet the quota set by…

A: T(x, y)=x4+16y4-32xy+43Tx =4x3+0-32y(1)+0Tx=4x3-32yTxx =12x2-0Txx =12 x2Ty…

Q: In an economic enterprise, the total amount T that is produced is a function of the amount n of a…

A: (a) The graph of the function is as follows: (b) Here, T(1.02)=-2(1.02)3+3(1.02)2+1.02…

Q: Find the orthogonal trajectories of the family of curves. (Use C for any needed constant.) y² . 5kx3…

A: We have to find orthogonal trajectories of the family of the curves y2=5kx3.

Q: Suppose a company has fixed costs of $12,300 and variable cost per unit of $0.20 x+128 dollars,…

A:

Q: 8. Determine a quadratic function f(x) = ax² + bx + c if its graph passes through the point (2,22)…

A:

Q: Find the orthogonal trajectories of the family of curves x2+y2=a2

A: We have to find the orthogonal trajectories of the family of curves x2+y2=a2.

Q: In a certain company, the income from the sale of x thousand pieces of products is given by I (x) =…

A: We first try to find the profit function.  Profit= Income - Cost…

Q: Find the maximum and minimum values of the function y=4x^(3)−4x+6 on the interval [0,2]. (Use…

A:

Q: The line tangent to the graph of g(x) = x³ – 4x +1 at the point (2, 1) is given by the formula L(x)…

A:

Q: Given the function y = 8e-²x² + 7 sec² 5x – 4 ln x³, find y'. Solution: y' = 4(3)x² x³3 +8(−4x)e-²x²…

A: We will find the y' of the given function in the following step.