Name: Ridley

Who is asking: Student
Level: Secondary

Question: I cannot figure out the following problem. Please help. Suppose a function f(x) has the line 3x+4y=2 as its tangent line at x=5. Find f'(5).

Thank you.

The tangent line to y = f(x) at x = 5 is the line through (5,f(5)) with slope f'(5). Since the line 3x + 4y = 2 is this tangent line its slope must be f'(5). Write the equation of the line 3x + 4y = 2 in the form y = mx + b and then f'(5) = m.