Home › TS EAPCET (Engineering) › Mathematics › Application of Derivatives › For f(x) = x³ on [0, 2], the mean value theorem …
For f(x) = x³ on [0, 2], the mean value theorem gives which value of c in (0, 2)?
A1/√3
B√2
C2/√3
D4/3
Answer & Solution
Correct answer: C. 2/√3
The average slope is 8/2 = 4, so 3c² = 4 and c = 2/√3, which lies inside (0, 2).
Related questions
The function f(x) = |x - 2| has its minimum at x = 2, where its derivativeAmong rectangles of area 100 cm^2, the least possible perimeter isThe largest area of a rectangle that can be inscribed in a circle of radius r isFor y = x^2, x changes from 10 to 10.1. The differential dy isUsing differentials, the approximate value of √25.1 isOn the interval (0, π), the function cos x isThe curve y = ln x on (0, infinity) isThe point of inflection of f(x) = x^3 - 6x^2 + 9x lies at x equal to