One A y = e^x dy/dx = e^x The f(x) = the differentiated function. Any value that e^x can have, the derivative has the same value. x is contained in all the reals. One B y = x*e^x y' = e^x + xe^x Using the multiplication rule. You want the slope and the value of the of y to be the same. The slope is y' of the tangent line xe^x = e^x + xe^x e^x = 0 This happens only when x is very "small" like x = - 4444444
y = e^x * ln(x) Using the multiplication rule again, we need the slope of the line with is y' y1 = e^x y1' = e^x y2 = ln(x) y2' = 1/x y' = e^x*ln(x) + e^x/x So at x = 1 the slope of the line = y' = e^1*ln(1) + e^1/1 y' = e*0+e = e y = mx + b y = ex + b to find b we use y= e^x ln(x)
e^x ln(x) = e*x + b e^1 ln(1) = e*1 + b ln(1) = 0 0 = e + b b = - e
