Question

# The equation of the tangent to the curve $$\displaystyle \mathrm{y}=\mathrm{x}+\frac{4}{\mathrm{x}^{2}}$$ , that is parallel to the $$x-axis$$, is

A
y=1
B
y=2
C
y=3
D
y=0

Solution

## The correct option is C $$\mathrm{y}=3$$ $$\displaystyle {y}={x}+\frac{4}{x^{2}}$$ $$\Rightarrow \displaystyle \frac{dy}{dx}=1-\frac{8}{x^{3}}$$Since, tangent is parallel to x-axis i.e. $$\displaystyle \frac{dy}{dx}=0$$$$0=1-\dfrac{8}{x^3}$$$$x^3=8$$$$\Rightarrow x=2$$substitute in the equation of the curve$$y=2+\dfrac{4}{2^2}=2+\dfrac{4}{4}=2+1$$$$\Rightarrow y=3$$        .Equation of tangent is given as $${y}-3=0({x}-2)$$   [slope-point form]$$\Rightarrow y-3=0$$ Hence, option 'C' is correct.Mathematics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More