Question

If the tangent to the curve y=x(x-1) at the point (a,b) is parallel to the X-axis, then

Answer 1

$\textbf{Given:}$

$\textsf{Curve is}\;\mathsf{y=x(x-1)}$

$\textbf{To find:}$

$\textsf{The condition that the tangent to the curve at (a,b) is parallel to x-axis}$

$\textbf{Solution:}$

$\mathsf{Consider,}$

$\mathsf{y=x(x-1)}$

$\implies\mathsf{y=x^2-x}$

$\textsf{Differentiate with respect to x}$

$\mathsf{\dfrac{dy}{dx}=2x-1}$

$\mathsf{Slope\;of\;tangent\;at\;(a,b)}$

$\mathsf{=\left(\dfrac{dy}{dx}\right)_{(a,b)}}$

$\mathsf{=2a-1}$

$\textsf{Since the tangent is parallel to x-axis, }$

$\textsf{slope of tangent is 0}$

$\implies\mathsf{2a-1=0}$

$\implies\mathsf{2a=1}$

$\implies\boxed{\mathsf{a=\dfrac{1}{2}}}$

$\textbf{Find more:}$

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