Home
Class 12
MATHS
Let f(x)a n dg(x) be differentiable for ...

Let `f(x)a n dg(x)` be differentiable for `0lt=xlt=2` such that `f(0)=2,g(0)=1,a n df(2)=8.` Let there exist a real number `c` in `[0,2]` such that `f^(prime)(c)=3g^(prime)(c)dot` Then find the value of `g(2)dot`

A

2

B

3

C

4

D

5

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS ENGLISH|Exercise EXAMPLE|6 Videos

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS ENGLISH|Exercise SINGLE OPTION CORRECT TYPE QUESTIONS|9 Videos

  • DIFFERENTIATION

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 10|4 Videos

  • ELLIPSE

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|27 Videos

Similar Questions

Explore conceptually related problems

Let f(x)a n dg(x) be differentiable for 0lt=xlt=1, such that f(0)=0,g(0)=0,f(1)=6. Let there exists real number c in (0,1) such taht f^(prime)(c)=2g^(prime)(c)dot Then the value of g(1) must be 1 (b) 3 (c) -2 (d) -1

Let f(x)a n dg(x) be differentiable for 0lt=xlt=1, such that f(0)=0,g(0)=0,f(1)=6. Let there exists real number c in (0,1) such that f^(prime)(c)=2g^(prime)(c)dot Then the value of g(1) must be (a) 1 (b) 3 (c) -2 (d) -1

Let fa n dg be differentiable on [0,1] such that f(0)=2,g(0)=0,f(1)=6a n dg(1)=2. Show that there exists c in (0,1) such that f^(prime)(c)=2g^(prime)(c)dot

If f(x)a n dg(x) are differentiable functions for 0lt=xlt=1 such that f(0)=10 ,g(0)=2,f(1)=2,g(1)=4, then in the interval (0,1)dot (a) f^(prime)(x)=0 for a l lx (b) f^(prime)(x)+4g^(prime)(x)=0 for at least one x (c) f(x)=2g'(x) for at most one x (d) none of these

If f(x)a n dg(x) are differentiable functions for 0lt=xlt=1 such that f(0)=10 ,g(0)=2,f(1)=2,g(1)=4, then in the interval (0,1)dot (a) f^(prime)(x)=0 for a l lx (b) f^(prime)(x)+4g^(prime)(x)=0 for at least one x (c) f(x)=2g'(x) for at most one x (d) none of these

Let f(x)a n dg(x) be two differentiable functions in Ra n df(2)=8,g(2)=0,f(4)=10 ,a n dg(4)=8. Then prove that g^(prime)(x)=4f^(prime)(x) for at least one x in (2,4)dot

Let f(x)a n dg(x) be two differentiable functions in R a n d f(2)=8,g(2)=0,f(4)=10 ,a n dg(4)=8. Then prove that g^(prime)(x)=4f^(prime)(x) for at least one x in (2,4)dot

Statement 1: If both functions f(t)a n dg(t) are continuous on the closed interval [a,b], differentiable on the open interval (a,b) and g^(prime)(t) is not zero on that open interval, then there exists some c in (a , b) such that (f^(prime)(c))/(g^(prime)(c))=(f(b)-f(a))/(g(b)-g(a)) Statement 2: If f(t)a n dg(t) are continuous and differentiable in [a, b], then there exists some c in (a,b) such that f^(prime)(c)=(f(b)-f(a))/(b-a)a n dg^(prime)(c)(g(b)-g(a))/(b-a) from Lagranges mean value theorem.

Let g: RvecR be a differentiable function satisfying g(x)=g(y)g(x-y)AAx , y in R and g^(prime)(0)=aa n dg^(prime)(3)=bdot Then find the value of g^(prime)(-3)dot

Let g: RvecR be a differentiable function satisfying g(x)=g(y)g(x-y)AAx , y in R and g^(prime)(0)=aa n dg^(prime)(3)=bdot Then find the value of g^(prime)(-3)dot