4 votes 4 votes 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. No solution $x \in (0, 1)$ More than one solution $x \in (0, 1)$ Exactly one solution $x \in (0, 1)$ At least one solution $x \in (0, 1)$ Set Theory & Algebra tifrmaths2015 set-theory&algebra functions + – makhdoom ghaya asked Dec 21, 2015 makhdoom ghaya 469 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 1 votes 1 votes 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). Shivansh Gupta answered Aug 25, 2016 selected Dec 19, 2017 by Arpit Dhuriya Shivansh Gupta comment Share Follow See all 0 reply Please log in or register to add a comment.