Question

Let f(x) = square root of x. Find c if the rate of change of f at x = c is twice the rate of change at x = 1.

a) c = 0.25
b) c = 0.5
c) c = 1
d) c = 4

Answer 1

To find c, compare the rate of change at x = c and x = 1. The rate of change at x = c is given by the derivative, f'(x) = 1/(2√x).

the correct answer is: d) c = 4

Step-by-step explanation:

To find c, we need to compare the rate of change at x = c and x = 1. The rate of change of f at x = c is given by the derivative, f'(x). Since f(x) = √x, the derivative is f'(x) = 1/(2√x). We can set up an equation to compare the rates of change:

1/(2√c) = 2 * 1/(2√1)

Simplifying the equation, we get 1/(√c) = 1/√1

Since the square root of 1 is 1, the equation becomes 1/(√c) = 1

Cross-multiplying, we get √c = 1

Squaring both sides of the equation, we get c = 1