Implicit derivative Consider the function defined implicitly by the following equation y? = x3 + 6x2...

 

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Implicit derivative Consider the function defined implicitly by the following equation y? = x3 + 6x2 { y^2 = x^3+ 6x^2 Differentiate implicitly to find dy/dx Solve for the location of all horizontal tangent lines. Solve for the location of all vertical tangent lines. QUESTION 6 10 Derivative of Inverse Consider the function f(x) defined by the following f(x) = (2x - 4)^3 } a) Find the inverse and sketch both graphs on the coordinate system. State the relationship between these graphs. b) Verify the relation between the slope of the tangent line to f(x) at a=3 and the slope of the tangent line to its inverse at b = 8. %3! QUESTION 7 Derivative of Inverse consider th function defined implicitly by the following equation { y^2 x = x^3 - y^3 - 2x + 4y + 5 } a) Differentiate implicitly to find dy/dx. b) Find the inverse function by using the substitution x <-> y Then differentiate implicitly to find its derivative. Observe the relation between the derivative of the function and its inverse. QUESTION 8 derivative of logarithm First use the rules for logarithms to simplify the logarithm on the right-hand side of the equal sign. Then take the derivative. x3 e5x y = In x² +1 Implicit derivative Consider the function defined implicitly by the following equation y? = x3 + 6x2 { y^2 = x^3+ 6x^2 Differentiate implicitly to find dy/dx Solve for the location of all horizontal tangent lines. Solve for the location of all vertical tangent lines. QUESTION 6 10 Derivative of Inverse Consider the function f(x) defined by the following f(x) = (2x - 4)^3 } a) Find the inverse and sketch both graphs on the coordinate system. State the relationship between these graphs. b) Verify the relation between the slope of the tangent line to f(x) at a=3 and the slope of the tangent line to its inverse at b = 8. %3! QUESTION 7 Derivative of Inverse consider th function defined implicitly by the following equation { y^2 x = x^3 - y^3 - 2x + 4y + 5 } a) Differentiate implicitly to find dy/dx. b) Find the inverse function by using the substitution x <-> y Then differentiate implicitly to find its derivative. Observe the relation between the derivative of the function and its inverse. QUESTION 8 derivative of logarithm First use the rules for logarithms to simplify the logarithm on the right-hand side of the equal sign. Then take the derivative. x3 e5x y = In x² +1