JEE Main 2014MathematicsApplication of DerivativesMediumMCQ

JEE Main 2014 — Application of Derivatives Question with Solution

JEE Main 2014 (09 Apr Online)

Question

If fx=35x+45x-1, x∈R, then the equation fx=0 has :

Choose an option

Show full solutionCorrect option: C
Correct answer
COne solution

Step-by-step explanation



f'x=35xln35+45xln45<0 ∀ x∈R

∵ddxax=axlna

Hence, fx is monotonically decreasing.

Also, limx→+∞fx→-1 ∵limx→∞ax=0, 0<a<1

and limx→-∞fx→∞   ∵limx→-∞ax=∞, 0<a<1

and there is only 1 solution for fx=0.

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About this question

This is a previous-year question from JEE Main 2014, covering the Application of Derivatives chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.