suppose the function f is defined so that f(0)=1 and its derivative is given by f'(x)=e^sinx. which of the following are true? options in description

Question

1. f''(0)=1 2. the line y=x+1 is tangent to the graph of f at x=0 3. if h(x)=f(x^3 -1), then h is increasing for all real numbers x.

Answer 1

f'' = cosxe^sinx ... f''(0)=1 thus 1) is true ...

f'(0)=1 and f(0)=1 so the tangent line = y=x+1 thus 2) is true

f' =e^sin(x^3-1) is >0 for all real x, thus 3) is true