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The number of points in (-oo,oo), for wh...

The number of points in `(-oo,oo),` for which `x^2-xsinx-cosx=0,` is

A

6

B

4

C

2

D

0

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The correct Answer is:
C
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Let A (0,2),B and C be points on parabola y^(2)+x +4 such that /_CBA (pi)/(2) . Then the range of ordinate of C is (a) (-oo,0)uu (4,oo) (b) (-oo,0] uu[4,oo) (c) [0,4] (d) (-oo,0)uu [4,oo)

Let f(x) lt 0 AA x in (-oo, 0) and f (x) gt 0 AA x in (0,oo) also f (0)=0, Again f'(x) lt 0 AA x in (-oo, -1) and f '(x) gt 0 AA x in (-1,oo) also f '(-1)=0 given lim _(x to -oo) f (x)=0 and lim _(x to oo) f (x)=oo and function is twice differentiable. The minimum number of points where f'(x) is zero is: (a) 1 (b) 2 (c) 3 (d) 4

The range of a for which the equation x^2+ax-4=0 has its smaller root in the interval (-1,2)i s a. (-oo,-3) b. (0,3) c. (0,oo) d. (-oo,-3)uu(0,oo)

The solution of system of linear inequalities in x represented on line as (i) x in ( - oo,-4) cup [3,oo) (ii) x in (- oo, -4] cup (5,oo) (iii) x in (- oo , -3) cup (5,oo) (iv) x in (-oo , -4) cup [ 5,oo)

Let f be the function f(x)=cosx-(1-(x^2)/2)dot Then (a) f(x) is an increasing function in (0,oo) (b) f(x) is a decreasing function in (-oo,oo) (c) f(x) is an increasing function in (-oo,oo) (d) f(x) is a decreasing function in (-oo,0)

RESONANCE ENGLISH-APPLICATION OF DERIVATIVES-Exersise-3 Part I
  1. If f(x) is a polynomial of degree 4 having extremum at x=1,2 and lim(x...

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  2. Let f be a function defined on R (the set of all real numbers) such th...

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  3. Let f,g and h be real-valued functions defined on the interval [0,1] b...

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  4. The number of distinct real roots of x^4-4x^3+12 x 62+x-1=0i sdot

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  5. Let p(x) be a real polynomial of least degree which has a local maximu...

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  6. Let I RvecI R be defined as f(x)=|x|++x^2-1|dot The total number of po...

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  7. The number of points in (-oo,oo), for which x^2-xsinx-cosx=0, is

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  8. A rectangular sheet of fixed perimeter with sides having their lengths...

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  9. A vertical line passing through the point (h, 0) intersects the ellips...

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  10. The funciton f(X) =2|x|+|x+2|-||x+2|-|x|| has a local mimimum or a lo...

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  11. Let f:[0,1]rarrR be a function. Suppose the function f is twice differ...

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  12. Let a in R and let f: Rvec be given by f(x)=x^5-5x+a , then (a) f(x...

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  13. The slope of the tangent to the curve (y-x^5)^2=x(1+x^2)^2 at the poin...

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  14. A cylindrical container is to be made from certain solid material with...

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  15. Let f,g:[-1,2]vecR be continuous functions which are twice differentia...

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  16. Let f:Rrarr(0,oo)andg:RrarrR be twice differentiable functions such th...

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  17. If f:R->R is a twice differentiable function such that f''(x) > 0 for ...

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  18. If f:R is a differentiable fucntion such that f(x) gt 2f(x) for all x...

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  19. If f(x) = \begin{vmatrix} cos2x & cos2x & sin2x \\ -cosx & cosx & -...

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  20. For every twice differentiable function f: R to [-2,2] with (f^(0))^(2...

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