Maxima and minima

 $\frac{\text{d}y}{\text{d}x}=0$  , of the tangent at a point P(x,y) on the curve is parallel to the x-axis 

• True

• False 

If  $\frac{\text{d}y}{\text{d}x}=\infty$  , then the tangent at a point P(x,y) on the curve is perpendicular to the x- axis. 

• False 

• True 

The maximum or minimum point are called the turning or stationary point.

• True

• False

For minimum point (i)  $\frac{\text{d}y}{\text{d}x}=0$  
(ii)  $\frac{\text{d}y}{\text{d}x}$  changes sign from -ve to +ve 

• False

• True

For Maximum point : (i)  $\frac{\text{d}x}{\text{d}y}=0$ ; (ii)  $\frac{d^2y}{dx^2}$  < 0

• False

• True

The point at which the function has neither maximum or minimum value is called

• Point of infraction

• Point of inflation

• Point of iridescence

• Point of inflection

Find the maximum and minimum value of - | x-2 | + 5

• Maximum value 5 no minimum value

• no maximum no minimum value

• maximum value 5 & minimum value 0

• maximum value 7 & minimum value 2

Find maximum and minimum value for x+1 in [-1,1]

• 1,-1

• 2,0

• no maximum no minimum value

• only maximum value i.e. 2

If the derivative of a function changes sign from negative to positive as we go from left to right of a point, then then the point will be of

• Local Maxima

• Local Minima

The function f(x) = log sinx is strictly increasing on (0, pi/2)

• True

• False