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If y= 6x - x^(3) and x increases at the ...

If `y= 6x - x^(3)` and x increases at the rate of 5 units/sec the rate of change of slope when x =3 is

A

`-90` units/sec

B

90 units/sec

C

180 units/sec

D

`-180` units/sec

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The correct Answer is:
A
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PREMIERS PUBLISHERS-APPLICATIONS OF DIFFERENTIAL CALCULUS-Problems For Practice (Choose the correct answer)
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  2. Which of the following is concave down:

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  3. If f(a) = 2, f'(a) = 1, g(a) = -1, g' (a) = 2. Then underset(x rarr a)...

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  4. The velocity v of a particle moving along a straight line when at a di...

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  5. The value of c in Lagrange's mean value theorem for the function f(x) ...

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  6. The function f(x) = x^(2) is decreasing in

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  7. y = -e^(x) is

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  8. If f has a local extremum at a and if f'(a) exists then

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  9. A spherical snowball is melting in such a way that its volume is decre...

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  10. f(x) = sqrtx, a = 1, b = 4 find c in Lagrange's mean value theorm:

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  11. The point of curve y= 2x^(2) - 6x -4 at which the tangent is paral...

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  12. The curve y = 3e^(x) and y = (a)/(3) e^(-x) intersect orthogonally if ...

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  13. f'(x) = x^(2) - 5x + 4 then f(x) is decreasing in

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  14. If the normal to the curve x^(2//3)+y^(2//3)=a^(2//3) makes an angle t...

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  15. For the curve x = e^(t) cos t, y = e^(t) sin t the tangent line is par...

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  16. If y= 6x - x^(3) and x increases at the rate of 5 units/sec the rate o...

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  17. If the length of the diagonal of a square is increasing at the rate of...

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  18. The equation of the normal to the curve theta = (1)/(t) " at " (-3, (-...

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  19. The point of inflection of the curve y = x^(4) is at:

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  20. The angle between the curve y = e^(mx) and y = e^(-mx) m gt 1 is

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