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Find the least value of the function `f(x)=x^3-18 x^2+96 x` in the interval `[0,9]` is ?

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To find the least value of the function \( f(x) = x^3 - 18x^2 + 96x \) in the interval \([0, 9]\), we can follow these steps: ### Step 1: Differentiate the function We start by finding the derivative of the function \( f(x) \). \[ f'(x) = \frac{d}{dx}(x^3 - 18x^2 + 96x) \] ...
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NCERT EXEMPLAR ENGLISH-APPLICATION OF DERIVATIVES-OBJECTIVE TYPES QUESTIONS
  1. If y=x^4-12 and if x changes from 2 to 1.99. what is the appoinmate ch...

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  2. Find the equation of the tangent to the curve (1+x^2)y=2-x , where it ...

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  3. The points at which the tangents to the curve y=x^(3)-12x+18 are paral...

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  4. The tangent to the curve y=e^(k x) at a point (0,1) meets the x-axis a...

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  5. The slope of the tangent to the curve x=t^2+3t-8,\ \ y=2t^2-2t-5 at ...

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  6. What is the angle between these two curves x^3-3xy^2+2=0 and 3x^2y-y^3...

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  7. 24. Find the intervals in which the following function is (a) increasi...

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  8. The function f:R rarr R be defined by f(x)=2x+cosx then f

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  9. If y=x(x-3)^(2) decreases for the values of x given by

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  10. The function f(x) =4sin^(3)x-6sin^(2)x +12 sinx + 100 is strictly

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  11. Which of the following functions are decreasing on (0,\ pi//2) ? (i) c...

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  12. The function f(x)= tan x - x

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  13. If x is real, then the minimum value of the expression x^2-8x+17 is

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  14. Find the least value of the function f(x)=x^3-18 x^2+96 x in the inter...

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  15. Show that the least value of the function f(x)=2x^3-3x^2-12x+1 on [-2,...

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  16. Show that The maximum value of sinx. cosx in R is 1/2

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  17. At x=(5pi)/6,\ \ f(x)=2sin3x+3cos3x is (a) 0 (b) maximum (c) minimum (...

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  18. The maximum slope of curve y =-x^(3)+3x^(2)+9x-27 is

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  19. The function f(x)=x^(x) has a stationary point at

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  20. Show that the maximum value of (1/x)^x is e^(1//e) .

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