Question

For the function f(x) = 8x², determine f'(1) using the formula f'(x) = limₕ→0 f(x + h) - f(x) / h. Choose the correct value for f'(1):

A. 16
B. 8
C. 24
D. 0

Answer 1

To find the derivative of the function f(x) = 8x² and determine f'(1), we can use the limit definition of derivative. By substituting x = 1 into the derivative formula and calculating the limit, we find that f'(1) = 16.

Step-by-step explanation:

To find the derivative of the function f(x) = 8x², we can use the formula f'(x) = limₕ→0 (f(x + h) - f(x)) / h. Let's substitute x = 1 into the formula and calculate the limit:

f'(1) = limₕ→0 (f(1 + h) - f(1)) / h = limₕ→0 (8(1 + h)² - 8) / h

Expanding and simplifying the expression, we get:

f'(1) = limₕ→0 (8h² + 16h) / h = limₕ→0 (8h + 16) = 16

Therefore, the value of f'(1) is 16. So, the correct answer is A. 16.