Question

Help , I will give medals !!!!

Suppose that the function f has a continuous second derivative for all x, and that f(0)=2 , f'(0)=-3 and f''(0)=0. Let g be a function whose derivative is given by g'(x)=e^-2x(3f(x)+2f'(x)) for all x

a) write the equation of the line tangent to the graph of f at the point where x=o

b) is there sufficient information to determine whether or not the graph of f has a point of inflection when x=0? explain your answer

c) given that g(0)=4, write an equation of the line tangent to the graph o g at the point where x=0

Answer 1

d) show that g''(x)=e^-2x(-6f(x)-f'(x)+2''(x))