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Consider the following.3x + 3y = 8(a) Find y' by implicit differentiation.(b) Solve the equation explicitly for y and differentiate to get y' in terms of x.(c) Check that your solutions to part (a) and (b) are consistent by substituting the expression for y into your solution for part (a).y' =

Answer :

lublana

Answer:

a.y'=-1

b.y'=-1

c.Yes

Step-by-step explanation:

We are given that consider a function

[tex]3x+3y=8[/tex]

Implicit function: That function is a relation in which dependent variable can not be expressed in terms of independent variable

Explicit function: It is that function in which dependent variable can be expressed in terms of independent variable.

a.[tex]3x+3y=8[/tex]

Differentiate w.r.t x then we get

[tex]3+3\frac{dy}{dx}=0[/tex]

[tex]3\frac{dy}{dx}=-3[/tex]

[tex]\frac{dy}[dx}=\frac{-3}{3}=-1[/tex]

[tex]\frac{dy}{dx}=y'=-1[/tex]

b.[tex]3x+3y=8[/tex]

[tex]3y=8-3x[/tex]

[tex]y=\frac{8-3x}{3}[/tex]

Differentiate w.r.t x then we get

[tex]\frac{dy}{dx}=\frac{-3}{3}=-1[/tex]

[tex]\frac{dy}{dx}=y'=-1[/tex]

When we substituting the value of y obtained from part b into a solution of part a then we get

[tex]y'=-1[/tex]

Hence, solutions are consistent.

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