AP Calculus AB Question

Question

The figure above shows the graph of the differential equation function g and the line tangent to the graph of g at the point (5,2). Let f be the function given f(x)=integral x, 0 g(t)dt let h be the function with first derivative given by h’(x)=x^2sin (x/3) for 0<x<7. If the line tangent to the graph of h at x=a is parallel to the line tangent to the graph of f at x=5 what is the value of a?

Answer 1

the tangent to f(x) at x=5 is g(5)=2 since f is intergral of g,,,f' is g

so want a²sin(a/3)=2

graphing x²sin(x/3)-2=j(x)

x=1.86 approximately makes j(x)=0

a=1.86 approximately