wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Using Rolle's theorem, find points on the curve y = 16 − x2, x ∈ [−1, 1], where tangent is parallel to x-axis.

Open in App
Solution

The equation of the curve is
y=16-x2. ...(1)

Let Px1,y1 be a point on it where the tangent is parallel to the x-axis.

Then,
dydxP=0 ...(2)

Differentiating (1) with respect to x, we get

dydx=-2xdydxP=-2x1-2x1=0 from 2x1=0

Px1, y1 lies on the curve y=16-x2.

y1=16-x12

When x1=0,
y1=16

Hence, 0, 16 is the required point.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Theorems
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon