The derivative of a function f is given by f′(x)=0.1x+e0.25x. At what value of x for x>0 does the line tangent to the graph of f at x have slope 2 ?

X=2.287

Step-by-step explanation:

Since the derivative gives you lines which are tangent to the graph f(x), you can find the slope of the line tangent through the equation of the derivative. Set 2 equal to the derivative and you will get 2=0.1x+e^0.25x (assuming you meant e^0.25x not e*0.25x in your question). Using a graphing calculator in order to find the answer graphically, find at what x are the two equations y=2 and y=0.1x+e^0.25x are equal. The result is x=2.287.

table 3 represents a direct variation function. : )