0

Guest

Courses New

Suppose that f is differentiable for all x and that f ′(x) ≤ 2 for all x. If f(1) = 2 and f(4) = 8, then f(2) has the value equal to………

Suppose that f is differentiable for all x and that
f ′(x) ≤ 2 for all x. If f(1) = 2 and f(4) = 8, then f(2)
has the value equal to………

Grade:12

2 Answers

Ronak Jain
16 Points
11 years ago

Given f'(x)<=2

Integrate both side, we'll get f(x)=2x+C

From Given , f(1)=2(1)+C=2 

We Get C=0;

Also F(4)=2(4)+0 = 8 (Given)

Thus F(2)=2(2)=4

 

Please Reply if i am Wrong.

aniket anil mandavkar
17 Points
11 years ago

Using LMVT for f in [1, 2]
2 1
(2) (1)
−
f − f = f ′(c) ≤ 2 ⇒ f (2) – f (1) ≤ 2
⇒ f(2) ≤ 4
Using LMVT for f in [2, 4]
4 2
(4) (2)
−
f − f = f ′(d) ≤ 2 and proceed

 

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on Differential Calculus

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More