Aspire Faculty ID #3631 · Topic: NIMCET 2012 · Just now
NIMCET 2012

The point on the curve $y = 6x - x^2$ where the tangent is parallel to the x-axis is:

Solution

Tangent ∥ x-axis ⇒ slope = 0 
Differentiate: $\dfrac{dy}{dx} = 6 - 2x$ 
Set derivative equal to zero: 
$6 - 2x = 0$ $2x = 6$ 
$x = 3$ 
Now find $y$: 
$y = 6(3) - (3)^2 = 18 - 9 = 9$ 
Therefore, the required point is $(3,9)$.
Answer: $(3,9)$
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