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# Solution for Using Rolle'S Theorem, Find Points on the Curve Y = 16 − X2, X ∈ [−1, 1], Where Tangent is Parallel to X-axis. - CBSE (Commerce) Class 12 - Mathematics

ConceptMaximum and Minimum Values of a Function in a Closed Interval

#### Question

Using Rolle's theorem, find points on the curve y = 16 − x2x ∈ [−1, 1], where tangent is parallel to x-axis.

#### Solution

The equation of the curve is

$y = 16 - x^2$  ...(1)

Let P

$\left( x_1 , y_1 \right)$ be a point on it where the tangent is parallel to the x-axis .
Then,
$\left( \frac{dy}{dx} \right)_P = 0$   ...(2)
Differentiating (1) with respect to x, we get

$\frac{dy}{dx} = - 2x$

$\Rightarrow \left( \frac{dy}{dx} \right)_P = - 2 x_1$

$\Rightarrow - 2 x_1 = 0 \left( \text { from } \left( 2 \right) \right)$

$\Rightarrow x_1 = 0$

$P\left( x_1 , y_1 \right)$  lies on the curve
$y = 16 - x^2$ .
$\therefore$ $y_1 = 16 - {x_1}^2$
When
$x_1 = 0$ ,
$y_1 = 16$

Hence,

$\left( 0, 16 \right)$ is the required point .
Is there an error in this question or solution?

#### APPEARS IN

Solution Using Rolle'S Theorem, Find Points on the Curve Y = 16 − X2, X ∈ [−1, 1], Where Tangent is Parallel to X-axis. Concept: Maximum and Minimum Values of a Function in a Closed Interval.
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