If a particle moves in a straight line according to s = t³-6t²-15t, the time interval during which the velocity is negative and acceleration is positive is __________

(a)

2 < t < 5

(b)

2 ≤ t ≤ 5

(c)

t ≥ 2

(d)

t ≤ 2

The equation of the tangent to the curve x = t cost, y = t sin t at the origin is __________

(a)

x = 0

(b)

y = 0

(c)

x +y = 0

(d)

x + y = 7

The function -3x+12 is ________ function on R.

(a)

decreasing

(b)

strictly decreasing

(c)

increasing

(d)

strictly increasing

\(\underset { x\rightarrow 0 }{ lim } \frac { x }{ tanx } \) is _________

(a)

1

(b)

-1

(c)

0

(d)

∞

The statement "If f has a local extremum at c and if f'(c) exists then f'(c) = 0" is ________

(a)

the extreme value theorem

(b)

Fermat's theorem

(c)

Law of mean

(d)

Rolle's theorem