7-8. Shape of the curve Sketch a curve with the following properties.

x < 3 f' < 0 and f" < 0

x > 3 f' < 0 and f" > 0

Solution: Step1 Given that x<3 f’(x)<0 and f’’(x)<0 x>3 f’(x)<0 and f’’(x)>0 If x<3 => f’(x)<0 Means f(x) is decreasing f’’(x)<0 means for all x in some interval I then f(x) is concave down on I. If x>3 => f’(x)<0 Means f(x) is decreasing. f’’(x)>0 means for all x in some interval I then f(x) is concave up on I. Step2 Sketch of curve from given data