The set of all real values of $$\lambda $$ for which the function

$$f(x) = \left( {1 - {{\cos }^2}x} \right)\left( {\lambda + \sin x} \right),x \in \left( { - {\pi \over 2},{\pi \over 2}} \right)$$

has exactly one maxima and exactly one minima, is :

The position of a moving car at time t is
given by f(t) = at² + bt + c, t > 0, where a, b and c are real numbers greater than 1. Then the average speed of the car over the time interval [t₁ , t₂ ] is attained at the point :

Which of the following points lies on the tangent to the curve

x⁴e^y + 2$$\sqrt {y + 1} $$ = 3 at the point (1, 0)?

If x = 1 is a critical point of the function
f(x) = (3x² + ax – 2 – a)e^x , then :