Let f be the function defined by f(x)=ex2.
(a) Calculate f′(x).
(b) Write the equation of the line tangent to the graph of f at x=0.5 in point–slope form and then simplify to slope–intercept form.
(c) Use the tangent line found in part (b) to approximate the value of f(0.51). Clearly show all work leading to your approximation.