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5. Find a point P on the graph of f(x) - In(x) so the tangent line to fat P goes through the origin. 6. x(t) = R.(t - sin(t) ), y(t) = R.(1 - cos(t) ) . (a) Find dx/dt, dy/dt, the tangent slope dy/dx, and speed when t = n/2 and n. 7. In problems a-c, you are given f'. Find a function f with the given derivative. a. f(x)=3sin?(x)cos(x) b)f(x) =5(1 + ex)*ex c)f(x)=e* + sinx 8.In problems a-c , use logarithmic differentiation to find dy/dx . Vx+ 10 x2 +1 a. y (2x+3)3(5x-1)7 b. y=(3 + sinx)* c ) y x 2 - 1 9. The graph of y = f'(x) is given in Fig. 12. (a) Assume f(0) = 0 and sketch the graph of y = f(x) . (b) Assume f(0) = 1 and graph y = f(x) . y = f'(x) Fig. 12 10. f(x) = x- + 2x, At which point(s) (p. f(p) ) does the line tangent to the graph at that point also go through the point (3, 6) ?"