



 
Hi Princess. The term f ′ (x) refers to the derivative of f(x). The derivative of f(x) is the slope of f(x). The slope of f(x) is the tangent line to f(x) at whatever value of x you are interested in. So f ′ (x) is itself the slope of f(x). This means 3x^{2} + 1 is the slope of x^{3} + x. By simply plugging in the value x = 1, you can find the slope of the tangent line. And of course f(x) is the y value corresponding to x, giving you a point on the tangent line (the point of tangency itself). The equation of any line, given a point on the line (x_{0}, y_{0}) and a slope m is:
Since the slope of a function f(x) is f ' (x) and the value y_{0} = f(x_{0}), the tangent line of any function f(x) at a particular value of x = x_{0} is:
Just substitute x_{0} = 1 and simplify to complete the question:
Cheers,  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 