intervals and whatever

Question

Answer 1

(5).

Caliculate the average rate of change of f(x) on the interval [a, b] by using formula : [f(b) - f(a)] / (b - a).

The function is f(x) = 3x² and interval is [0, 3].

f(b) = f(3) = 3*3² = 27.

f(a) = f(0) = 3*0² = 0.

Average rate of change = [f(b) - f(a)] / (b - a) = (27-0) / (3-0) = 9.

Answer 2

(6).

The equation is x² + xy = 10 and x = -1.

To find the y-value, substitute x = -1 in the above equation.

(-1)² + (-1)y = 10 ⇒ y = -9.

Differentiate with respect to x.

2x + x*y' + y= 10

y'= (10 - 2x - y)/x

Substitute x = -1 and y = -9 in the above equation.

y'= [10 - 2(-1) - (-9)] / (-1)

y' = - 21.