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The length of the longest interval in wh...

The length of the longest interval in which the function `3sinx-4sin^3x` is increasing, is

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CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Assertion Consider the following statements in SandR S: Both sinx and...

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  2. Let f(x)=int0^xe^t(t-1)(t-2)dt, Then f decreases in the interval

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  3. The length of the longest interval in which the function 3sinx-4sin^3x...

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  4. Tangent is drawn to ellipse (x^2)/(27)+y^2=1 at (3sqrt(3)costheta,sint...

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  5. If f(x)=xe^(x(1-x)) , then f(x) is(a) increasing on [−1/2,1] (b) decr...

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  6. Let f(x)=(1+b^2)x^2+2b x+1 and let m(b) the minimum value of f(x) as b...

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  7. Suppose that f is a polynomial of degree 3 and that f^(x)!=0 at any...

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  8. The maximum value of the function f(x)=((1+x)^(0. 6))/(1+x^(0. 6)) in ...

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  9. The value of a for which the functionf(x)=asinx+1/3sin3x has an extrem...

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  10. If f(x)=(t+3x-x^2)/(x-4), where t is a parameter that has minimum and ...

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  11. A factory D is to be connected by a road with a straight railway line ...

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  12. Let f(x)=ax^3+bx^2+cx+1 has exterma at x=alpha,beta such that alpha ...

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  13. Consider the function f(x)=xcosx-sinxdot Then identify the statement w...

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  14. The number of values of k for which the equation x^3-3x+k=0 has two di...

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  15. The least natural number a for which x+a x^(-2)>2AAx in (0,oo) is 1 (b...

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  16. A function f is defined by f(x)=|x|^m|x-1|^nAAx in Rdot The local max...

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  17. A rectangle of the greatest area is inscribed in a trapezium A B C D ,...

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  18. f(x)={4x-x^3+ln(a^2-3a+3),0lt=x<3 x-18 ,xgeq3 complete set of values...

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  19. Let the function f(x) be defined as follows:(x)= {x^3 +x^2 −10x,−1≤x<...

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  20. A differentiable function f(x) has a relative minimum at x=0. Then the...

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