Question

What is the best estimate of the instantaneous rate of hange for the function f(x)= square root 8x at the point of x = 8?
1. 2square root 2/ squareroot8
2. 1
3. 2square root 2
4. 1/2

Answer 1

d/dx [ a b] = adb/dx + b da/dx
d/dx (8^n * x^n) = 8^n * n x^(n-1) + x^n * 0
so
d/dx (8 x)^.5 = 8^.5 * .5 x^-.5
= 8^.5 * .5 / 8^.5
= .5