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If f(x)=x^3+b x^2+c x+d and 0<b^2<c , th...

If `f(x)=x^3+b x^2+c x+d` and `0

A

is bounded

B

has a local maxima

C

has a local minima

D

is strictly increasing

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The correct Answer is:
D
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TARGET PUBLICATION-APPLICATIONS OF DERIVATIVES-COMPETITIVE THINKING
  1. Suppose the cubic x^3-px+q has three real roots where pgt0 and qgt0 . ...

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

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  3. Let f:""RvecR be defined by f(x)""={k-2x , if""xlt=-1 2x+3,f""x >-1} ....

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  4. For x epsilon(0,(5pi)/2), definite f(x)=int(0)^(x)sqrt(t) sin t dt. T...

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

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  6. If f(x)={{:(x",",0lexle1),(2-e^(x-1)",",1ltxle2),(x-e",",2ltxle3):} an...

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  7. e total number of local maxima and local minima of the function f(x) =...

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  8. Let f(x)=(1+b^(2))x^(2)+2bx+1 and let m(b) be the minimum value of f ...

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  9. Given P(x) =x^(4) +ax^(3) +bx^(2) +cx +d such that x=0 is the only re...

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

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  11. The points on the curve y=12x-x^3 at which the gradient is zero are

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  12. The displacement of a particle at time t is x, where x=t^4-kt^3. IF th...

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  13. If f(x) satifies of conditiohns of Rolle's theorem in [1,2] and f(x) i...

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  14. IF f(x)=x,-1lexle1, then function f(x) is

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  15. If f(x)=x^3+b x^2+c x+d and 0<b^2<c , then f(x) is a strictly increasi...

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

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  17. Let f(x) be a polynomial of degree four having extreme values at x=1 a...

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  18. if Agt0,Bgt0 and A+B=pi/3 then the maximum value of tanA.tanB is (A) 1...

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  19. A wire of length 2 units is cut into two parts which are bent respe...

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  20. Consider f(x)=tan^(-1)(sqrt((1+sinx)/(1-sinx))), x in (0,pi/2)dot A n...

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