Question:

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

Updated On: Jul 5, 2022
  • $y = 1$
  • $y = 2$
  • $y = 3$
  • $y = 0$
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The Correct Option is C

Solution and Explanation

Parallel to x-axis $\quad\Rightarrow \frac{dy}{dx} = 0\quad\Rightarrow1-\frac{8}{x^{3}} = 0$ $\Rightarrow x = 2\quad\Rightarrow y = 3$ Equation of tangent is $y - 3 = 0\left(x - 2\right)\quad\Rightarrow y - 3 = 0 $
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Concepts Used:

Application of Derivatives

Various Applications of Derivatives-

Rate of Change of Quantities:

If some other quantity ‘y’ causes some change in a quantity of surely ‘x’, in view of the fact that an equation of the form y = f(x) gets consistently pleased, i.e, ‘y’ is a function of ‘x’ then the rate of change of ‘y’ related to ‘x’ is to be given by 

\(\frac{\triangle y}{\triangle x}=\frac{y_2-y_1}{x_2-x_1}\)

This is also known to be as the Average Rate of Change.

Increasing and Decreasing Function:

Consider y = f(x) be a differentiable function (whose derivative exists at all points in the domain) in an interval x = (a,b).

  • If for any two points x1 and x2 in the interval x such a manner that x1 < x2, there holds an inequality f(x1) ≤ f(x2); then the function f(x) is known as increasing in this interval.
  • Likewise, if for any two points x1 and x2 in the interval x such a manner that x1 < x2, there holds an inequality f(x1) ≥ f(x2); then the function f(x) is known as decreasing in this interval.
  • The functions are commonly known as strictly increasing or decreasing functions, given the inequalities are strict: f(x1) < f(x2) for strictly increasing and f(x1) > f(x2) for strictly decreasing.

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