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Let f(x) be defined as f(x)={tan^(-1)alp...

Let `f(x)` be defined as `f(x)={tan^(-1)alpha-5x^2,0

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The correct Answer is:
`alpha lt -tan 1`
`f(x)={{:(tan^(-1) alpha-5x^(2),0ltxlt),(-6x,xge1):}`
f(1)=-6
for maximum at x=1
`underset(xrarr1)lim f(x)=tan^(-1)alpha -5lt-6`
or `tan^(-1)alphalt-1 or alpha-tan 1`
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CENGAGE ENGLISH-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Concept Application Exercise 6.4
  1. Find the least value of secA+secB+secC in an acute angled triangle.

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  2. Find the critical (stationary ) points of the function f(X)=(x^(5))/(2...

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  3. The curve f(x)=(x^2+a x+b)/(x-10) has a stationary point at (4,1) . Fi...

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  4. If the function f(x) =axe^(bx^(2)) has maximum value at x=2 such that ...

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  5. Discuss the extremum of f(x)=1/3(x+1/x)

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  6. Discuss the extremum of f(x)=1+2sinx+3 cos^2x ,xlt=xlt=(2pi)/3

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  7. Discuss the extremum of f(x)=sinx+1/2sin2x+1/3sin3x ,0lt=xlt=pidot

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  8. Let f(x)=-sin^3x+3sin^2x+5on[0,pi/2] . Find the local maximum and loca...

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  9. discuss the extremum of f(theta)=sin^pthetacos^qtheta, p , q gt0,0ltth...

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  10. Find the maximum and minimum values of the function y=(log)e(3x^4-2x^3...

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  11. Discuss the extremum of f(x)=x(x^2-4)^(-1/3)

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  12. Discuss the maxima and minima of the function f(x)=x^(2/3)-x^(4/3)dot ...

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  13. Discuss the extremum of f(x)={|x^2-2|, -1lt=x<sqrt(3)x/(sqrt(3)), sqr...

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  14. Discuss the extremum of f(x)={1+sinx ,x<0x^2-x+1,xgeq0a tx=0

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  15. Find the minimum value of |x|+|x+1/2|+|x-3|+|x-5/2|dot

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  16. Let f(x) be defined as f(x)={tan^(-1)alpha-5x^2,0<x<1-6x ,xgeq1 If f(...

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  17. Let f(x)={x^3-x^2+10 x-5,xlt=1, \ -2x+(log)2(b^2-2),x >1 Find the val...

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