Question

For what value of a is f'(a) = 1/4 the tangent line for f(x) = x² at x = 0?

A) a = 1/8
B) a = 1/4
C) a = 1/2
D) a = 1

Answer 1

To find the value of a for which f'(a) is equal to 1/4, we need to solve the equation 2a = 1/4, leading to a = 1/8.

Step-by-step explanation:

To find the value of a, we need to determine when the derivative of the function f(x) = x² is equal to 1/4, which represents the slope of the tangent line at x = 0.

First, we find the derivative of f(x): f'(x) = 2x.

Next, we substitute a into the derivative: f'(a) = 2a.

Finally, we set f'(a) equal to 1/4 and solve for a:

2a = 1/4
a = 1/8