Solve the following question.

Question

Find the value of x at which the graphs of f(x)=x^2-5x+4 and g(x)=-2x+3 have parallel tangent lines.

Answer 1

The derivative of f(x) gives the slope of the tangent line of f(x) at any point x. Likewise, the derivative of g(x) gives the slope of the tangent line of f(x) at any point x. So if you want to know where the slopes are the same (parallel lines) then set them equal and solve for x.

f '(x) = 2x - 5

g'(x) = -2

2x - 5 = -2

2x = 3

x = 3/2

So at x = 3/2, the slopes of the tangent lines are both the same. (-2)