Solution for problem 8E Chapter 4.3
Solved: Shape of the curve Sketch a curve with the
Calculus: Early Transcendentals | 1st Edition
7-8. Shape of the curve Sketch a curve with the following properties.
x < -1 f' < 0 and f" < 0
-1 < x < 2 f' < 0 and f" > 0
2 < x < 8 f' > 0 and f" > 0
8 < x < 10 f' > 0 and f" < 0
x > 10 f' > 0 and f” > 0
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
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Solved: Shape of the curve Sketch a curve with the