Application of Derivatives 3 Question 1

####1. If $f: R \rightarrow R$ is a twice differentiable function such that $f^{\prime \prime}(x)>0$ for all $x \in R$, and $f \frac{1}{2}=\frac{1}{2}, f(1)=1$, then

(a) $f^{\prime}(1) \leq 0$

(b) $f^{\prime}(1)>1$

(c) $0<f^{\prime}(1) \leq \frac{1}{2}$

(d) $\frac{1}{2}<f^{\prime}(1) \leq 1$

(2017 Adv.)

Show Answer

Answer:

Correct Answer: 1. (b)

Solution:

  1. $f^{\prime}(x)$ is increasing

For some $x$ in $\frac{1}{2}, 1$

$ f^{\prime}(x)=1 $

$ \therefore \quad f^{\prime}(1)>1 $

[LMVT]



NCERT Chapter Video Solution

Dual Pane