मराठी

At What Point on the Following Curve, is the Tangent Parallel to X-axis Y = X2 on [−2, 2] ?

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प्रश्न

At what point  on the following curve, is the tangent parallel to x-axis y = x2 on [−2, 2]
?

बेरीज
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उत्तर

Let \[f\left( x \right) = x^2\]

Since \[f\left( x \right)\] is a polynomial function, it is continuous on \[\left[ - 2, 2 \right]\] and differentiable on \[\left( - 2, 2 \right)\] .

Also, \[f\left( 2 \right) = f\left( - 2 \right) = 4\]
Thus, all the conditions of Rolle's theorem are satisfied.
Consequently, there exists at least one point c
\[\in \left( - 2, 2 \right)\] for which  \[f'\left( c \right) = 0\] .
But \[f'\left( c \right) = 0 \Rightarrow 2c = 0 \Rightarrow c = 0\]
\[\therefore f\left( c \right) = f\left( 0 \right) = 0\]
By the geometrical interpretation of Rolle's theorem, \[\left( 0, 0 \right)\] is the point on \[y = x^2\] , where the tangent is parallel to the x-axis.
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पाठ 14: Mean Value Theorems - Exercise 15.1 [पृष्ठ ९]

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आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
पाठ 14 Mean Value Theorems
Exercise 15.1 | Q 8.1 | पृष्ठ ९

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