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Let a in R and let f: R to R be given b...

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

A

f(x) has three real roots if a `gt4`

B

f(x) has only one real root is `a gt 4`

C

f(x) has three real roots if `a lt -4`

D

f(x) has three real roots if `-4 lt a lt4`

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The correct Answer is:
B, D
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RESONANCE-APPLICATION OF DERIVATIVES-Exersise-3 Part I
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  6. Let f[0, 1] -> R (the set of all real numbers be a function.Suppose t...

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  7. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

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  8. line L:y=mx+3 meets y–axis at E(0, 3) and the are of the parabola y^(2...

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

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

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  11. A cylindrica container is to be made from certain solid material with ...

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  12. Let f,g:[-1,2]rarr RR be continuous functions which are twice differen...

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  13. Let f: R to (0 ,oo)" and " g :R to R be twice differentiable function...

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  14. Which of the following options is the only INCORRECT combination ?

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  15. Which of the following options is the only CORRECT combination

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  16. Which of the following options is the only CORRECT combination ?

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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:RR-> RR is a differentiable function such that f(x) > 2f(x) f...

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  19. then

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

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