Shape of the curve ?Sketch a curve with the following properties.
Solution: Step1 x 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. -1 f’(x)<0 and f’’(x)>0 If -1 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 20 and f’’(x)>0 If 2 f’(x)>0 Means f(x) is increasing f’’(x)>0 means for all x in some interval I then f(x) is concave up on I. 8 f’(x)>0 and f’’(x)<0 If 8 f’(x)>0 Means f(x) is increasing. f’’(x)<0 means for all x in some interval I then f(x) is concave down on I. x>10=> f’(x)>0 and f’’(x)>0 If x>10=> f’(x)>0 Means f(x) is increasing. f’’(x)<0 means for all x in some interval I then f(x) is concave up on I. Step3
