The curves of the quadratic and cubic functions are f(x)=2x-x^2 and g(x)= ax^3 +bx^2+cx+d. where a,b,c,d...

The curves of the quadratic and cubic functions are f(x)=2x-x^2 and g(x)= ax^3 +bx^2+cx+d. where a,b,c,d ER, intersect at 2 points P and Q. These points are also two points of tangency for the two tangent lines drawn from point A(2,9) upon the parobala. The graph of the cubic function has a y-intercept at (0,-1) and an x intercept at (-4,0). What is the standard equation of the tangent line AP.

Expert Solution

milcah answered 1 year ago

The curves of the quadratic and cubic functions are f(x)=2x-x^2 and g(x)= ax^3 +bx^2+cx+d. where a,b,c,d...

The curves of the quadratic and cubic functions are f(x)=2x-x^2 and g(x)= ax^3 +bx^2+cx+d. where a,b,c,d ER, intersect at 2 points P and Q. These points are also two points of tangency for the two tangent lines drawn from point A(2,9) upon the parobala. The graph of the cubic function has a y-intercept at (0,-1) and an x intercept at (-4,0). What is the value of the coefficient "b" in the equation of the given cubic function.

1. Consider the cubic function f ( x ) = ax^3 + bx^2 + cx +...

1. Consider the cubic function f ( x ) = ax^3 + bx^2 + cx + d where a ≠ 0. Show that f can have zero, one, or two critical numbers and give an example of each case. 2. Use Rolle's Theorem to prove that if f ′ ( x ) = 0 for all xin an interval ( a , b ), then f is constant on ( a , b ). 3.True or False. The product of...

Find the cubic equation. F(x)=ax^3+bx^2+cx+d F(-1)=3 F(1)=1 F(2)=6 F(3)=7 What is the value of a,b,c,d

Given a general cubic function y = ax^3 + bx^2 + cx + d prove the...

Given a general cubic function y = ax^3 + bx^2 + cx + d prove the following, a) That a cubic must change at a quadratic rate. I believe this to be the derivative of the general cubic function, yielding dy/dx = 3ax^2 + 3bx + c b) That there are only 6 basic forms (shapes) for a cubic. This question is where I get lost. Please help, Thanks!

Find the cubic equation: f(x) = ax^3+bx^2+cx+d for which f(-1)=3, f(1)=1, f(2)=6, and f(3)=7. Find the...

Find the cubic equation: f(x) = ax^3+bx^2+cx+d for which f(-1)=3, f(1)=1, f(2)=6, and f(3)=7. Find the value of a, b, c, and d

1. Solve quadratic equation Ax^2+Bx+C=0 using the quadratic formula x = (-B+ and - sqrt(B^2-4ac)) /...

1. Solve quadratic equation Ax^2+Bx+C=0 using the quadratic formula x = (-B+ and - sqrt(B^2-4ac)) / 2a) and output the two solution with clear explanation could you please do it in MATLAB

use Java The two roots of a quadratic equation ax^2 + bx + c = 0...

use Java The two roots of a quadratic equation ax^2 + bx + c = 0 can be obtained using the following formula: r1 = (-b + sqrt(b^2 - 4ac)) / (2a) and r2 = (-b - sqrt(b^2 - 4ac)) / (2a) b^2 - 4ac is called the discriminant of the quadratic equation. If it is positive, the equation has two real roots. If it is zero, the equation has one root. If it is negative, the equation has no...

FOR JAVA Define a class QuadraticExpression that represents the quadratic expression ax^2 + bx + c:...

FOR JAVA Define a class QuadraticExpression that represents the quadratic expression ax^2 + bx + c: You should provide the following methods (1) default constructor which initalizes all the coefficients to 0 (2) a constructor that takes three parameters public QuadraticExpression(double a, double b, double c) (3) a toString() method that returns the expression as a string. (4) evaluate method that returns the value of the expression at x public double evaluate(double x) (5) set method of a, b, c...

1114) intg{ 2x ln(x^2) dx } = (Ax^B)*(ln(x^2)+F) + C. Determine A,B,F. ans:3 1130) Evaluate intg_9_17{...

1114) intg{ 2x ln(x^2) dx } = (Ax^B)*(ln(x^2)+F) + C. Determine A,B,F. ans:3 1130) Evaluate intg_9_17{ (x^2 - 4x + 7) dx }. ans:1 1132) Integrate from 3 to 7 the function: ( 1 / (x^2 + 9x) ). Calculate a floating-point value. ans:1

B= {1,x,x^2} B’={1-x^2, x-x^2, 1+2x-x^2} T(a+bx+cx^2) = 3a+b+c+(2a+4b+2c)x + (-a-b+c)x^2 a) by direct calculation , compute...

B= {1,x,x^2} B’={1-x^2, x-x^2, 1+2x-x^2} T(a+bx+cx^2) = 3a+b+c+(2a+4b+2c)x + (-a-b+c)x^2 a) by direct calculation , compute [P]_B’ , p=7-x+2x^2 b) using basis B={1,x,x^2} , compute [T]_B c_ compute [T]_B’

Question

The curves of the quadratic and cubic functions are f(x)=2x-x^2 and g(x)= ax^3 +bx^2+cx+d. where a,b,c,d...

Solutions

Expert Solution

Related Solutions

The curves of the quadratic and cubic functions are f(x)=2x-x^2 and g(x)= ax^3 +bx^2+cx+d. where a,b,c,d...

1. Consider the cubic function f ( x ) = ax^3 + bx^2 + cx +...

Find the cubic equation. F(x)=ax^3+bx^2+cx+d F(-1)=3 F(1)=1 F(2)=6 F(3)=7 What is the value of a,b,c,d

Given a general cubic function y = ax^3 + bx^2 + cx + d prove the...

Find the cubic equation: f(x) = ax^3+bx^2+cx+d for which f(-1)=3, f(1)=1, f(2)=6, and f(3)=7. Find the...

1. Solve quadratic equation Ax^2+Bx+C=0 using the quadratic formula x = (-B+ and - sqrt(B^2-4ac)) /...

use Java The two roots of a quadratic equation ax^2 + bx + c = 0...

FOR JAVA Define a class QuadraticExpression that represents the quadratic expression ax^2 + bx + c:...

1114) intg{ 2x ln(x^2) dx } = (Ax^B)*(ln(x^2)+F) + C. Determine A,B,F. ans:3 1130) Evaluate intg_9_17{...

B= {1,x,x^2} B’={1-x^2, x-x^2, 1+2x-x^2} T(a+bx+cx^2) = 3a+b+c+(2a+4b+2c)x + (-a-b+c)x^2 a) by direct calculation , compute...