Start Free Mock LoginAlready registered? Login here

Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMonotonicity-Rolle's-theroemMedium2 minQB

MathematicsMediumnumerical

A thrice-differentiable $f$ on $R$ has at least five distinct zeros. Find the minimum guaranteed number of zeros of $f + 6 f' + 12 f'' + 8 f'''$ .

Answer:

2.00

Solution:

Set $g = e^{x /2} f$ . Five zeros of $g$ yield at least two zeros of $g'''$ after three applications of Rolle. Since $8 e^{- x /2} g''' =$ $f + 6 f' + 12 f'' + 8 f'''$ , at least two zeros are guaranteed.

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Monotonicity-Rolle's-theroem

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...