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At an extreme point of a function f(X) t...

At an extreme point of a function f(X) the tangent to the curve is

A

parallel to the x axis

B

perpendicular to the x axis

C

inclined at an angle `45^(@)` to the x axis

D

inclined at an angle `60^(@)` to the x axis

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Verified by Experts

The correct Answer is:
A
At an extreme point of a function f(X) slope is always zero
thus At an extreme point of a function f(X) the tangent to the curve is parallel to the axis
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NDA PREVIOUS YEARS-APPLICATION OF DERIVATIVES -Example
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  2. The function y=f(x)=mx+c has

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  3. At an extreme point of a function f(X) the tangent to the curve is

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  4. The point in the interval [0,2pi] where f(x) =e^(x) sinx has maximum s...

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  5. If the rate of change in volume of spherical soap bubble is uniform th...

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  6. If f(X)=x ln x then f(x) attains minumum value at which one of the fol...

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  7. Find the points on the curve x^2+y^2-2x-3=0at which the tangents are ...

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  8. Which of the following statement is correct ?

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  9. How many tangents are parallel to X-axis for the curve y = x^2 - 4x + ...

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  10. What is the rate of change of sqrt(x^(2)+16) with respect to x^(2) at ...

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

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  12. Which one of the following statement is correct ?

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

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

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

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

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

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

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

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

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