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Which one of the following statement is ...

Which one of the following statement is correct ?

A

`e^(x)` is an increasing funciton

B

`e^(x)` is a decreasing function

C

`e^(x)` is neither in increasing n or decreasing function

D

`e^(x)` is a constant function

Text Solution

Verified by Experts

The correct Answer is:
A

From the graph of `e^(x)` it is clear that `e^(x)` is an increasing function
Also Domain =R
and Range=`R^(+)`
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NDA PREVIOUS YEARS-APPLICATION OF DERIVATIVES -Example
  1. What is the rate of change of sqrt(x^(2)+16) with respect to x^(2) at ...

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

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  3. Which one of the following statement is correct ?

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  4. The radius of a circle is increasing uniformly at the rate of 3 cm/...

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  5. The function f(x)=x^(3)-3x^(2)+6 is an increasing funciton for :

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  6. What is the minimum value of |x|?

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  7. The function f(x)=x^(2)-4x, x in [0,4] attains minimum value at

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  8. The curve y =xe^(x) has minimum value equal to

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  9. The maximum value of the function f(x)=x^(3)+2x^(2)-4x+6 exits at

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  10. The minimum value of the function F(x)=|x-4| exists at

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  11. What is the slope of the tangent to the curve y=sin^(1)(sin^(2)x)

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  12. Consider the curve y=e^(2x) What is the slope of the tangent to the ...

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  13. The tangent to the curve y=e^(2x) at the point (0,1) meets X-axis at

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  14. Consider the function f(X)=(x^(2)-x+1)/(x^(2)+x+1) What is the maxim...

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  15. Consider the function f(X)=(x^(2)-x+1)/(x^(2)+x+1) What is the minim...

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  16. A rectangular box is to be made form a sheet of 24 inch length and 9 ...

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  17. A rectangular box is to be made form a sheet of 24 inch length and 9 ...

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  18. Show that the height of the cylinder of maximum volume that can be ...

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  19. A cylinder is inscribed in a sphere of radius r What is the radius o...

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  20. Consider the following statements 1. y=(e^(x)+e^(-x))/(2) is an incr...

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