Suppose that f(x) = 2x / (2−5x)^3. Find an equation for the tangent line to the graph of f at x=2. Tangent line: y = ?

Answer 1

f(2) = 2·2/(2 - 5·2)³ = - 1/128;

f'(x) = [2(2-5x)³- 2x·3(2 - 5x)²(- 5)]/(2 - 5x)⁶ = (4 + 20x)/(2 - 5x)⁴.

Slope of tangent line m = f'(2) = 44/(- 8)⁴ = 11/1024

Equation of tangent line: y = - 1/128 + 11/1024(x - 2) = 11/1024x - 15/512