word problem and equation

Question

Answer 1

6)

x² +xy =10

Take derivative both sides with respect to x.

d/dx (x² +xy ) = d/dx (10 )

d/dx (x²) +d/dx (xy) =0

Use product rule of derivatives.

2x  + x d/dx (y) +y d/dx (x) =0

2x  + x dy/dx + y=0

dy/dx = - ( y + 2x ) / x       ------ (1)

Find the y value when x = -1.

(-1)² +(-1)y =10

-y = 9

y = -9

Substitute x = -1 and y = -9 in equation (1).

dy/dx = - ( -9 + 2(-1) ) / (-1)

          = - 11

Answer 2

Find the average rate of change f (x) = 3x² in interval of  [0 , 3] by using the formula :

Average rate of change =[ f(b) - f(a) ] / (b - a)

                                      =[ f(3) - f(0) ] / (3 - 0)

                                      = [3(3)² - 3(0)²]/3

                                      = 27/3

                                      = 9