## 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

**Accepted Solution**

**Step 1 of 3**

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

**Step 2 of 3**

**Step 3 of 3**

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Solved: Shape of the curve Sketch a curve with the