The expression dy/dx = x(cube root^3 y) gives the slope at any point on the graph of the function f(x) where f(2) = 8. - equation of the tangent line f(x) at point (2,8) = (y-8)=4(x-2) - expression for f(x) in terms of x = f(x)=[x^2/3+8/3]^3/2 -domain all real numbers. -minimum [8/3]^3/2 Using the axes provided, sketch a slope field for the given differential equation at the nine points indicated.

Q: Reflect  f(x)=2x^2+3x-1 over the X axis and write the new equation for g

A: Reflect  f(x)=2x2+3x-1 over the X axis and write the new equation for g

Q: Equation is f(x)=3x-x^2

A: First we find out the slope of tangent line at x=2 and then the equation of the tangent line is…

Q: The given family of functions is the general solution of the differential equation on the indicated…

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Q: X, Y interceptes and graph the function  f(x)=-(x-2)^3+1

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Q: g(x)=√3-x State the domain for the function and it's derivative using interview notation

A: We have to find the domain for the given function and it's derivative

Q: Determine the equation of the oblique asymptote of the equation f(x)=2x^2-9x+10/2x-1

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Q: X^4+y^2=3 find the slope of the function above at (1,-sqrt2)

A: Explanation of the solution is given below....

Q: Find the slope of f(x)= (x^2-1)-(2x-3) at x=2

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Q: Find Domain and range of f(x)=x^x and graph it.

A: The objective is to find Domain and range of f(x)=x^x and graph it.

Q: Calculate the value of f(-3) for the function f(x) = 3x^2

A: In order to find the value of a function f(x) at a point x=a, we just replace a at the place of x…

Q: The first derivative of a function is y1=x^2-x-6. Use this derivative and the second derivative of…

A: Consider the given derivative and equate it to zero to determine the critical points for function y.…

Q: Find f”(x) for the function f(x)= -4x^2-4x-9

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Q: Choose the function that expresses the relationship 15x+5y^(3)=4 as a function, y=f(x), if possible.

A: To choose the function that expresses the relationship 15x+5y3=4 as a function y=f(x).

Q: y = (x^(2) -1)^(3) Analyze the function

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Q: f(x)=(x-3)^2-1 find the x-intercepts

A: To find x intercepts we have to plug f(x)=0

Q: Find the Harmonic conjugate of 3x^2 y-y^3 and construct the respective analytic function.

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Q: F(x)=x^4- 16 find the intercepts of the function

A: To find the y-intercept we plug x=0 and solve for F(x).

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.