Question: Calculus: Tangent Lines Find the equation of the tangent line of the curve tan(2x+5y) = x at (0,0). Pick ONE option
y = 5x
y = x/5
We have to find the equation of the tangent line of the curve
at the point (0,0).
Now, to find this, we have to find the value of
which is the slope of the tangent line, at a given point.
Differentiating both sides with respect to x, we get
Putting the value of x=0 and y=0, we can say that
So, the slope of the tangent will be -(1/5).
Now, at the point (0,0), the equation of the straight line is
So, the correct answer is option (D) .