| Assertion [A]: The tangent to the curve \[y={{x}^{3}}-{{x}^{2}}-x+2\] at (1, 1) is parallel to the X-axis. |
| Reason [R]: The slope of the tangent to the above curve at (1, 1) is zero. |
A) Both A and R are individually true and R is the correct explanation of A.
B) Both A and R are individually true and R is not the correct explanation of A.
C) 'A' is true but 'R' is false
D) 'A' is false but 'R' is true
E) Both A and R are false.
Correct Answer: A
Solution :
\[\frac{dy}{dx}=3{{x}^{2}}-2x-1\] At \[(1,1),\left( \frac{dy}{dx} \right)=3\times {{(1)}^{2}}-2\times 1-1=3-2-1=0\] \[\Rightarrow \] Slope of tangent \[=0\Rightarrow \]tangent is parallel to axis \[\Rightarrow \] Assertion [A] is true. Reason [R] is true and is correct explanation of A. Hence option [A] is the correct answer.
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