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Statement 1: If 27 a+9b+3c+d=0, then the...

Statement 1: If `27 a+9b+3c+d=0,` then the equation `f(x)=4a x^3+3b x^2+2c x+d=0` has at least one real root lying between `(0,3)dot` Statement 2: If `f(x)` is continuous in [a,b], derivable in `(a , b)` such that `f(a)=f(b),` then there exists at least one point `c in (a , b)` such that `f^(prime)(c)=0.`

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CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Statement 1: If both functions f(t)a n dg(t) are continuous on the clo...

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  2. Discuss monotonocity of y=f(x) which is griven by x=1/(1+t^2) and y=1...

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  3. Statement 1: If 27 a+9b+3c+d=0, then the equation f(x)=4a x^3+3b x^2+2...

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  4. Find the value of a for which the function (a+2)x^3-3a x^2+9a x-1 decr...

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  5. The angle of intersection between the curves y=[|sinx|+|cosx|]andx^2+y...

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  6. Find the value of a in order that f(x)=sqrt(3)sinx-cosx-2a x+b decreas...

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  7. Show that curves ax^2+by^2=1 and cx^2+dy^2=1 intersect orthogonally if...

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  8. Discuss the monotonocity of function f(x)=2log|x-1|-x^2+2x+3.

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  9. If the area of the triangle included between the axes and any tangent ...

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  10. Separate the intervals of monotonocity for the function f(x)=3cos^4x+1...

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  11. If the tangent at (x1,y1) to the curve x^3+y^3=a^3 meets the curve aga...

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  12. Separate the intervals of monotonocity for the function f(x)=3cos^4x+1...

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  13. Show that the segment of the tangent to the curve y=a/2I n((a+sqrt(a^2...

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  14. Separate the intervals of monotonocity for the function f(x)=((log)e x...

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  15. Prove that the equation of the normal to x^(2/3)+y^(2/3)=a^(2/3) is yc...

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  16. Discuss monotonocity of f(x)=x/(sinx)a n d g(x)=x/(tanx),where (xlt=1...

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  17. Prove that the curves y=f(x),[f(x)>0],a n dy=f(x)sinx ,w h e r ef(x) i...

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  18. Discuss the extremum of f(x)={x^2+x^-2}

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  19. Tangents are drawn from the origin to curve y=sinxdot Prove that point...

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  20. Write the maximum value of f(x)=x^(1//x) .

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