The slope of the curve y = e^xcos(x), x $\in \left(- \mathrm{\pi }, \mathrm{\pi }\right)$ is maximum at

• x = $\frac{\mathrm{\pi }}{2}$

• $\mathrm{x} = - \frac{\mathrm{\pi }}{2}$

• $\mathrm{x} = \frac{\mathrm{\pi }}{4}$

• x = 0

The equation of tangent to the curve y = x³ - 6x + 5 at (2, 1) is

• 6x - y - 11 = 0

• 6x - y - 13 = 0

• 6x + y + 11 = 0

• 6x - y + 11 = 0

Let f(x) = 2x³ - 5x² - 4x + 3, $\frac{1}{2} \le \mathrm{x} \le 3$. The point at which the tangent to the curve is parallel to the X-axis, is

• (1, - 4)

• (2, - 9)

• (2, - 4)

• (2, - 1)

Two sides of triangle are 8 m and 56 m in length. The angle between them is increasing at the rate 0.8=08  rad/s. When the angle between sides of fixed length is $\frac{\mathrm{\pi }}{3}$, the rate at which the area of the triangle is increasing, is

• 0. 4 m²/s

• 0.8 m²/s

• 0 . 6 m²/s

• 0.04 m²/s

If y = 8x³ - 60x² + 144x + 27 is a decreasing function in the interval

• (- 5, 6)

• $\left(- \infty , 2\right)$

• (5, 6)

• (2, 3)

The minimum value of the function max (x, x) is equal to

• 0

• 1

• 2

• 1/2

557.

Let f(x) = 2x³ - 9ax² + 12a²x + 1, where a > 0. The minimum of f is attained at a point q and the maximum is attained at a point p. If p = q, then a is equal to

• 1

• 3

• 2

• 0

The difference between the maximum and minimum value of of the function $\mathrm{f}\left(\mathrm{x}\right) = {\int }_0^{\mathrm{x}}\left({\mathrm{t}}^2 + \mathrm{t} + 1\right)\mathrm{dt}$ on [2, 3] is

• 39/6

• 49/6

• 59/6

• 69/6

If a and b are the non-zero distinct roots of x² + ax + b = 0, then the minimum value of x² + ax + b is

• 2/3

• 9/4

• - 9/4

• - 2/3

The equation of the tangent to the curve (1 + x²)y = 2 - x where it crosses the x-axis, is :

• x + 5y = 2

• x - 5y = 2

• 5x - y = 2

• 5x + y - 2 = 0