Question

Use the definition of the derivative to compute f'(c) for the given function. Use the results to determine an equation for the line tangent to the graph of f(x) at x = c. f(x) = 2√x; c = 25.

Answer 1

Answer: tangent line equation y = (1/5)x + 5

with f '(c) = 1/5

Explanation:

rewrite the function f(x) as f(x) = 2* x^(1/2)

f '(x) = 2* (1/2)* x^(1/2 - 1) = x^(-1/2)

we want f'(c) = f '(25) = (25)^(-1/2) = 1/5

slope of tangent line at x = c is 1/5

y - f(25) = (1/5)* (x - 25)

y - 10 = (1/5)* (x - 25)

y = (1/5)x - 5 + 10

y = (1/5)x + 5