COMEDK · Maths · 28. Indefinite Integration

If \(f(x)=x^n\) and \(f^{\prime}(1)=10\), then the value of ' \(n\) ' is

A 10
B 0
C 9
D 1

Verified Solution

Answer & Solution

Correct Answer

(A) 10

Step-by-step Solution

Detailed explanation

Given \(f(x) = x^{n}\). The derivative of \(f(x)\) with respect to \(x\) is \(f^{\prime}(x) = n x^{n-1}\). It is given that \(f^{\prime}(1) = 10\). Substituting \(x = 1\) into the derivative expression: \(f^{\prime}(1) = n(1)^{n-1} = n(1) = n\). Therefore, \(n = 10\). Answer: 10

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From COMEDK

A Hydrocarbon [A] (molecular formula \(\mathrm{C}_3 \mathrm{H}_6\)) on reaction with \(\mathrm{Br}_2 / \mathrm{CCl}_4\) gave [B]. When [B] is heated with 2 moles of alcoholic \(\mathrm{KOH}\), it gave compound [C]. 3 moles of Compound [C] when passed through red hot Iron tube forms [D]. Identify [D].

COMEDK 2024 Medium

Match the mixtures listed in Column I with the correct method used for their separation.

Column I	Column II
A. Glycerol from spent Lye	P. Steam distillation
B. Mixture of Benzoic acid and Naphthalene dissolved in organic solvent	Q. Distillation
C. Aniline & Chloroform	R. Distillation under reduced pressure
D. 2- Nitrophenol & 4- Nitrophenol	S. Differential extraction using \(\text{NaHCO}_3\)

COMEDK 2026 Medium

Explore more questions on app