mat 210

Find the indicated derivative using implicit differentiation. HINT [See Example 1.]

x²y − y² = 8; 

dy

dx

 

 

Find the indicated derivative using implicit differentiation. HINT [See Example 1.]

xe^y − ye^x = 5; 

dy

dx

 

 

Find the exact location of all the relative and absolute extrema of the function. HINT [See Example 1.]

g(t) = 

1

4

t⁴ − 

2

3

t³ + 

1

2

t² with domain (−∞, +∞)

g has       at 

(t, y) =  

 .

 

Find the exact location of all the relative and absolute extrema of the function. HINT [See Example 1.]

g(t) = e^t − t with domain [−1, 1]

g has       at 

(t, y) =  

 .

g has       at 

(t, y) =  

 .

g has       at 

(t, y) =  

 .