If f is a twice differentiable function ...

If f is a twice differentiable function such that `f''(x)=-f(x),f'(x)=g(x) ,h(x)=[f(x)]^2+[g(x)]^2` if h(5)=11, then h(10) equals

none of these

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

APPLICATION OF DERIVATIVES
PATHFINDER|Exercise QUESTION BANK|23 Videos

Similar Questions

Explore conceptually related problems

Let f be a twice differentiable function such that f"(x) = -f(x) , and f'(x) = g(x) , h(x)=[f(x)]^2+[g(x)]^2 Find h(10), if h(5) = 11

Let f be a differentiable function such that f(1) = 2 and f'(x) = f (x) for all x in R . If h(x)=f(f(x)) , then h'(1) is equal to

If f(x) is a twice differentiable function such that f(a)=0, f(b)=2, f(c)=-1,f(d)=2, f(e)=0 where a < b < c < de, then the minimum number of zeroes of g(x) = f'(x)^2+f''(x)f(x) in the interval [a, e] is

f(x) and g(x) are two differentiable functions on [0, 2] such that f''(x)-g''(x)=0, f'(1)=2, g'(1)=4, f(2)=3 and g(2)=9 , then [f(x)-g(x)] at x=(3)/(2) is equal to -

If f(x) and g(x) are twice differentiable functions on (0, 3) satisfying f''(x)=g''(x), f'(1)=4,g'(1)=6,f(2)=3,g(2)=9," then "f(1)-g(1) is -

If f(x) and g(x) are twice differentiable functions on (0,3) satisfying f"(x) = g"(x), f'(1) = 4, g'(1)=6,f(2)=3, g(2) = 9, then f(1)-g(1) is

If '' (x)=-f(x) and g(x)=-f'(x) and F(x)=(f(x/2))^2 + (g(x/2))^2 and given that f(5)=5, then f(10) is equal to

If f(x)=(a x^2+b)^3, then find the function g such that f(g(x))=g(f(x))dot

If f(x), g(x) be twice differentiable functions on [0,2] satisfying f''(x) = g''(x) , f'(1) = 2g'(1) = 4 and f(2) = 3 g(2) = 9 , then f(x)-g(x) at x = 4 equals (A) 0 (B) 10 (C) 8 (D) 2

Let f:R to R and h:R to R be differentiable functions such that f(x)=x^(3)+3x+2,g(f(x))=x and h(g(g(x)))=x for all x in R . Then, find the value of h'(1).

PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK

A value of ‘c’ for which conclusion of Mean Value Theorem holds for th...
Text Solution
|
If f(x)=x^3+bx^2+cx+d and 0ltb^2ltc then in (-oo,oo)
Text Solution
|
If f is a twice differentiable function such that f''(x)=-f(x),f'(x)=g...
Text Solution
|
Consider a function y = f(x) defined parametrically asy=2t+t, x=t^2 fo...
Text Solution
|
The range of value of x for which the function f(x)=x/logx,xgt0 and "x...
Text Solution
|
If F(x)=|[x,x^2,x^3],[1,2x,3x^2],[0,2,6x]| , then F'(x) is
Text Solution
|
The least value of the function f(x)= cos^(-1)x^2 in the interval [-1/...
Text Solution
|
If a function is everywhere continuous and differentiable such that f'...
Text Solution
|
If f'(x) exists for all x inR and g(x)=f(x)-(f(x))^2+(f(x))^3forallx i...
Text Solution
|
The set of all values of a for which the function f(x)=(sqrt(a+4)/(1...
Text Solution
|
The minimum value of the function defined by f(x)=max {x,x+1,2-x} is
Text Solution
|
If f(x)gt0 and f"(x)gt0 forallx in R, then for any two real numbers x1...
Text Solution
|
If 0ltalphaltbetaltpi/2 then
Text Solution
|
A function f is such that f'(4)=f''(4)=0 and f has minimum value 10 at...
Text Solution
|
If f(x)=x^2+2bx=2c^2 and g(x)=-x^2-2cx+b^2 are such that min f(x)gtmax...
Text Solution
|
If f(x)=x^alphalogx and f(0)=0, then the value of alpha for which Ro...
Text Solution
|
If 0ltxltpi/2,then
Text Solution
|
The number of values of x where the function f(x)=cosx+cos(sqrt2x) att...
Text Solution
|
The value of a so that the sum of the squares of the roots of the equa...
Text Solution
|
The equation e^(x-1)+x-2=0 as
Text Solution
|