The abscissa of the points of the curve y=x3 in the interval [–2, 2], where the slope of the tangents can be obtained by mean value theorem for the interval [–2, 2], are [MP PET 1993]
A
±2√3
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
±√3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
±√32
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
\N
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is A±2√3 According to the mean value theorem,
f'(c) = f(b)−f(a)b−a in the interval [a,b]
f'(c) = f(8)−f(−8)8+8
f'(c) = 4
Also, f'(c) = 3c2
so, 3c2 = 4
or c = ±2√3