Question

Let $f: R \rightarrow R$ be such that $f(0)=0$ and $\left|f^{\prime}(x)\right| \leq 5$ for all $x$. Then $f(1)$ is in
(A) $(5,6)$
(B) $[-5,5]$
(C) $(-\infty,-5) \cup(5, \infty)$
(D) $[-4,4]$

Answer 1

Ans: (B)
Hint : $\left|f^{\prime}(x)\right| \leq 5$
$$\begin{aligned} &\int_{0}^{1}-5 d x \leq \int_{0}^{1} f^{\prime}(x) d x \leq \int_{0}^{1} 5 d x \\ &\Rightarrow-5 \leq f(1)-0 \leq 5 \\ &\Rightarrow-5 \leq f(1) \leq 5 \\ &\Rightarrow f(1) \in[-5,5] \end{aligned}$$

Answer 2

buy cialis sale <a href="https://ordergnonline.com/">order cialis 40mg for sale</a> buy generic ed pills for sale