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BITSAT 2020
Exam
BITSAT
Year
2020
Subject
Mathematics
Chapter
Application of Derivatives

BITSAT 2020 · Mathematics · Application of Derivatives

Suppose that f(0)=-3 and f^ (x) ≤ 5 for all values of x Then, the...

Suppose that f(0)=−3f(0)=-3 and f′(x)≤5f^{\prime}(x) \leq 5 for all values of xx Then, the largest value which f(2)f(2) can attain is

Options

  1. A7
  2. B10
  3. C2
  4. D9

Correct answer

A. 7

Step-by-step solution

Using LMVT in [0,2] f(2)−f(0)2−0=f′(c),\frac{f(2)-f(0)}{2-0}=f^{\prime}(c), where c∈(0,2)f(2)+32≤5⇒f(2)≤7c \in(0,2)\frac{f(2)+3}{2} \leq 5 \Rightarrow f(2) \leq 7
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