Continuity And Differentiability

Question

If f and ga re differentiable functions in (0,1) satisfying f(0) =2= g(1), g(0) = 0 and f(1) = 6, then for some c ε] 0,1[

2f'(c) = g'(c)

2f'(c) = 3g'(c)

f'(c) = g'(c)

f'(c) = 2g'(c)

Solution

f'(c) = 2g'(c)

Given, f(0) = 2 = g(1), g(0) and f(1) = 6
f and g are differentiable in (0,1)
Let h(x) = f(x)-2g(x) .... (i)
h(0) = f(0)-2g(0)
h(0) = 2-0
h(0) = 2
and h(1) = f(1)-2g(1) = 6-2(2)
h(1) = 2, h(0) = h(1) = 2
Hence, using rolle's theorem
h'(c) = 0, such that cε (0,1)
Differentiating Eq. (i) at c, we get
f'(c) -2g'(c) = 0
f'(c) = 2g'(c)

For Daily Free Study Material Join wiredfaculty

Continuity And Differentiability

If f and ga re differentiable functions in (0,1) satisfying f(0) =2= g(1), g(0) = 0 and f(1) = 6, then for some c ε] 0,1[

2f'(c) = g'(c)

2f'(c) = 3g'(c)

f'(c) = g'(c)

f'(c) = 2g'(c)

Some More Questions From Continuity and Differentiability Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Location

For Daily Free Study Material Join wiredfaculty

Continuity And Differentiability

If f and ga re differentiable functions in (0,1) satisfying f(0) =2= g(1), g(0) = 0 and f(1) = 6, then for some c ε] 0,1[ 2f'(c) = g'(c) 2f'(c) = 3g'(c) f'(c) = g'(c) f'(c) = 2g'(c)

Some More Questions From Continuity and Differentiability Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

If f and ga re differentiable functions in (0,1) satisfying f(0) =2= g(1), g(0) = 0 and f(1) = 6, then for some c ε] 0,1[

2f'(c) = g'(c)

2f'(c) = 3g'(c)

f'(c) = g'(c)

f'(c) = 2g'(c)