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  • A particle moves along the curve . At what point on the curve is the tangent line parallel to

A particle moves along the curve y=4 x-x^2 . At what point on the curve is the tangent line parallel to the line y=2 x+1 ?

Option: 1

(1,3)


Option: 2

(2,4)


Option: 3

(-1,3)


Option: 4

(3,3)


Answers (1)

best_answer

The slope of the tangent line to the curve y=4 x-x^2at a point (x, y) is given by the derivative of y with respect to x, which is:

y^{\prime}=4-2 x

We want the tangent line to be parallel to the line y = 2x + 1, which has slope 2. Therefore, we need to find a point on the curve where y^{\prime}=4-2 x=2

Solving for x, we get

\begin{aligned} & 4-2 x=2 \\ & 2 x=2 \\ & x=1 \end{aligned}

So the point where the tangent line is parallel to y=2 x+1 \text { is }(1, y) is , where y=4(1)-1^2=3

Therefore, the answer is option (a)  \left ( 1,3 \right )

 

Posted by

Irshad Anwar

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