The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
x
+4 votes
138 views

Let $f: [0, 1]\rightarrow \mathbb{R}$ be a fixed continuous function such that $f$ is differentiable on $(0, 1)$ and $f(0) = f(1) = 0$. Then the equation $f(x) = f' (x)$ admits.

  1. No solution $x \in (0, 1)$
  2. More than one solution $x \in (0, 1)$
  3. Exactly one solution $x \in (0, 1)$
  4. At least one solution $x \in (0, 1)$
asked in Set Theory & Algebra by Boss (29.5k points) | 138 views

1 Answer

+1 vote
Best answer
Answer : D

all the conditions are given to hold the Rolle's theorem requisites,

hence f′(x) will be 0 for atleast 1 , which gives that f(x) = 0 from the given eqn. hence

f(x) has atleast 1 solution in (0,1).
answered by Active (2.6k points)
selected by

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
49,808 questions
54,481 answers
188,251 comments
74,530 users