Question

1. Use the first derivative test and the second derivative test to determine where each function...

1. Use the first derivative test and the second derivative test to determine where each function is​ increasing, decreasing, concave​ up, and concave down.

y=20x e^-x , x>0

2. Use the first derivative and the second derivative test to determine where each function is​ increasing, decreasing, concave​ up, and concave down.

y=4sin(πx^2), 10≤x≤1

Math   Calculus   
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Answer #1

1) Solution -

  

Differentiating both sides with respect to x

For increasing

  

So the function is increasing at

For decreasing

So the function is increasing at

Finding the second derivative

  

For concave up

  

Interval is

For concave down

  

  

Interval is  

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