The slope of the normal to the curve y = 2 x² + 3 sin x at x = 0 is

• 3

• 

• -3

• -3

The line y = x + 1 is a tangent to the curve y ² = 4x at the point

• (1, 2)

• (2, 3)

• (1, -2)

• (1, -2)

133. The normal at the point (1, 1) on the curve 2y + x² = 3 is

• x + y = 0
• x – y = 0
• x + y + 1 = 0
• x + y + 1 = 0

• x + y = 3 
• x – y = 3
• x + y = 1
• x + y = 1

Show that the function f(x) = x² is a decreasing function in (– ∞  0).

Construct an example of a functions which is strictly increasing but whose derivative vanishes at a point in the domain of definition of the function.

Prove that the exponential function e^x is strictly increasing on R.