please someone help me with this:
Consider the curve
The equation of the tangent line to the curve at the point has the form where
_________and _________________
please someone help me with this:
Consider the curve
The equation of the tangent line to the curve at the point has the form where
_________and _________________
Right for what? This makes no sense.
You are clearly confusing functions of several variables with functions of a single variable. To get the tangent to a curve defined by the relation f(x, y) = c you need to calculate dy/dx. To do this you either make y the subject (where possble or convenient) and differentiate or you just differentiate the relation using implicit differentiation and then solve for dy/dx. Either way, f(x, y) = c defines a function of a single variable.
i mean. if it's f(x) function(single variable) then i do not need to implicitly differentiate and just $\displaystyle F_{x}$ would give me m right?
Because it is a f(x y) function (several variable) so i have to implicit differentiate dy/dx to get m right?
You could think of the function as $\displaystyle x^6+2xf(x)+f^4(x)=4$.
That, you can see, is a function of one variable. If you could solve for $\displaystyle f(x)$, than you could just take a regular derivative, but since solving for $\displaystyle f(x)$ is either very hard or impossible, it makes the most sense to differentiate implicitly.