If f is twice differentiable such that f...

If `f` is twice differentiable such that `f''(x)=-f(x),` `f'(x)=g(x),` `h'(x)=[f(x)]^(2)+[g(x)]^(2)` and ` h(0)=2,` `h(1)=4,` then the equation `y=h(x)` represents.

a) a straight line with slope `2`

b) a straight line with y-intercept `1`

c) a straight line with x-intercept `2`

d) None of the above

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

MONOTONICITY MAXIMA AND MINIMA
ARIHANT MATHS|Exercise MAXIMA AND MINIMA EXERCISE 1|1 Videos
MONOTONICITY MAXIMA AND MINIMA
ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|19 Videos
MONOTONICITY MAXIMA AND MINIMA
ARIHANT MATHS|Exercise Exercise For Session 5|8 Videos
MATRICES
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|49 Videos
PAIR OF STRAIGHT LINES
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

Similar Questions

Explore conceptually related problems

Let f be a twice differentiable function such that f^(prime prime)(x)=-f(x),a n df^(prime)(x)=g(x),h(x)=[f(x)]^2+[g(x)]^2dot Find h(10)ifh(5)=11

Let f: (-1,1) rarr R be a differentiable function with f(0) = -1 and f'(0) = 1 let g(x) =[f(2f(x)+2)]^2 , then g'(0) =

If f(x)=sqrt(x^(2)+1),g(x)=(x+1)/(x^(2)+1) and h(x)=2x-3 , then find f'[h'{g'(x)}] .

Let f(x) and g(x) be differentiable functions such that f(x)+ int_(0)^(x) g(t)dt= sin x(cos x- sin x) and (f'(x))^(2)+ (g(x))^(2) = 1,"then" f(x) and g (x) respectively , can be

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(x))=x for all x in R . Then, h'(1) equals.

If f(x)=sinx,g(x)=x^(2)andh(x)=logx. IF F(x)=h(f(g(x))), then F'(x) is

Let y=f(x) be a differentiable function such that f(−1)=2,f(2)=−1 and f(5)=3 If the equation f (x)=2f(x) has real root. Then find f(x)

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

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2)(0)=1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .

ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (Single Option Correct Type Questions)

If m and n are positive integers and f(x) = int1^x(t-a )^(2n) (t-b)^(2...
Text Solution
|
Find the intervals in which the following function is increasing and d...
Text Solution
|
If f is twice differentiable such that f''(x)=-f(x), f'(x)=g(x), h'(x...
Text Solution
|
If f(x) ={:{(2x^2+2/x^2",",0ltabsxle2),(3",",x gt2):}then
Text Solution
|
Evaluate (n!)/((n - r)!) , when n = 4 , r = 3
Text Solution
|
sinx+cosx=y^2-y+a has no value of x for any value of y if a belongs to...
Text Solution
|
Evaluate (n!)/((n-r)!) , when n = 8 , r = 6
Text Solution
|
Suppose that f(x) is a quadratic expresson positive for all real xdot ...
Text Solution
|
Let f(x)=min{1,cos x,1-sinx}, -pi le x le pi, Then, f(x) is
Text Solution
|
Evaluate (5!)/((5 - 2)!)
Text Solution
|
Maximum number of real solution for the equation ax^(n)+x^(2)+bx+c=0...
Text Solution
|
Maximum number area of rectangle whose two points are are x=x(0),x=p...
Text Solution
|
f(x)=-1+kx+k neither touches nor intecepts the curve f(x)= Iog x, then...
Text Solution
|
f(x) is a polynomial of degree 4 with real coefficients such that f(x)...
Text Solution
|
A curve whose concavity is directly proportional to the logarithm of i...
Text Solution
|
f(x) = 4 tan x-tan^(2)x+tan^(3)x,xnenpi+(pi)/(2)
Text Solution
|
f (x)= {{:(3+|x-k|"," , x le k),(a ^(2) -2 + ( sin (x -k))/((x-k))"," ...
Text Solution
|
Let f(x) be linear functions with the properties that f(1) le f(2), f(...
Text Solution
|
If P(x) is polynomial satisfying P(x^(2))=x^(2)P(x)andP(0)=-2, P'(3//2...
Text Solution
|
Find the vertex and length of latus rectum of the parabola x^(2)=-4(y-...
Text Solution
|