MHT CET · Maths · Application of Derivatives
The abscissae of the points, where the tangent to curve \(y=x^{3}-3 x^{2}-9 x+5\) is parallel to \(x\) -axis, are
- A \(x=0\) and 0
- B \(x=1\) and \(-1\)
- C \(x=1\) and \(-3\)
- D \(x=-1\) and 3
Answer & Solution
Correct Answer
(D) \(x=-1\) and 3
Step-by-step Solution
Detailed explanation
Given, \(y=x^{3}-3 x^{2}-9 x+5\)
\(\Rightarrow \quad \frac{d y}{d x}=3 x^{2}-6 x-9\)
We know that, this equation gives the slope of the tangent to the curve. The tangent is parallel to \(x\) -axis, \(\frac{d y}{d x}=0\)
\(\Rightarrow \quad 3 x^{2}-6 x-9=0\)
\(\Rightarrow \quad x=-1,3\)
\(\Rightarrow \quad \frac{d y}{d x}=3 x^{2}-6 x-9\)
We know that, this equation gives the slope of the tangent to the curve. The tangent is parallel to \(x\) -axis, \(\frac{d y}{d x}=0\)
\(\Rightarrow \quad 3 x^{2}-6 x-9=0\)
\(\Rightarrow \quad x=-1,3\)
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