The equation of the tangent to the curve [y = x + 4 x^2], that is parallel to the x-axis, …

Question

The equation of the tangent to the curve $$y = x + {4 \over {{x^2}}}$$, that

is parallel to the $x$-axis, is

Accepted Answer

Since tangent is parallel to $x$-axis,

$$\therefore$$ $${{dy} \over {dx}} = 0 \Rightarrow 1 - {8 \over {{x^3}}} = 0 \Rightarrow x = 2 \Rightarrow y = 3$$

Equation of tangent is $$y - 3 = 0\left( {x - 2} \right) \Rightarrow y = 3$$

Solutions · 1