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Let f(x)=a(5)x^(5)+a(4)x^(4)+a(3)x^(3)+a...

Let `f(x)=a_(5)x^(5)+a_(4)x^(4)+a_(3)x^(3)+a_(2)x^(2)+a_(1)x, "where" a_(i),s` are real and f (x) = 0 has a positive root `alpha_(0).` Then `f^(prime)(x)=0` has a positive root `alpha_1` such that 0 < `alpha_1` < `alpha_0` `f^(prime)(x)=0` has at least two real roots `f^('')(x)=0` has at least one real root none of these

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CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
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  2. If f(x)a n dg(x) are two positive and increasing functions, then which...

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  3. Let f(x)=a(5)x^(5)+a(4)x^(4)+a(3)x^(3)+a(2)x^(2)+a(1)x, "where" a(i),s...

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  4. For the cubic function f(x)=2x^3+9x^2+12 x+1, which one of the followi...

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  5. If f(x)=(sin^2x-1)^("n"),"" then x=pi/2 is a point of local maximum, i...

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  6. Let f(x) be an decreasing function defined on (0,oo). If f(3a^2-4a+1)g...

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  7. In which of the following graphs is x=c the point of inflection?

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  8. L e tf(x)={((x-1)(6x-1))/(2x-1),ifx!=1/2 0,ifx=1/2 Then at x=1/2, whi...

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  9. If composite function f1(f2(f3((fn(x))))n timesis an decreasing functi...

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  10. The function (sin(x+a))/(sin(x+b)) has no maxima or minima if (a) b-a...

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  11. If varphi(x) is a polynomial function and varphi^(prime)(x)>varphi(x)A...

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  12. Which of the following statements is true for the function f(x)={sqrt(...

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  13. If f"(x)>0 for all x in R, f'(3)=0,and g(x)=f(tan^2 x-2tan x+4),0<x<pi...

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  14. Let f(x) be a function such that f'(x)=(log)(1/2)[(log)3(sinx+a)]dot ...

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  15. If f^(prime)(x)=|x|-{x}, where {x} denotes the fractional part of x , ...

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  16. Function f(x)=|x|-|x-1| is monotonically increasing when (a) x<0 (b) ...

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  17. Let f be continuous and differentiable function such that f(x) and f'...

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  18. If the function f(x) increases in the interval (a , b),a n dvarphi(x) ...

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  19. Let f be the function f(x)=cosx-(1-(x^2)/2)dot Then (a) f(x) is an inc...

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  20. If f(x)=x+sinx ,g(x)=e^(-x),u=sqrt(c+1)-sqrt(c), v=sqrt(c) -sqrt(c-1...

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