Answer the following question (AB CALC REVIEW)

Question

1) which of the following is an equation of the line tangent to the graph f(x)- (square root of x)-x at the point x=4? Explain why your answer choice is correct.

a) Y+2=-3/4(x-4)

b)y+2=-1/4(x-4)

c) y+2=1/4(x-4)

d) y+2=3/4(x-4)

2) Let f be the function given by f(x)=ln(2x). What is the instantaneous rate of change of f at x=4? Explain your answer with workout

Answer 1

In part 1) dy/dx at x=4 is ±1/4 and f(4)=-2; therefore ±1/4=(y+2)/(x-4).

In part 2) dy/dx = 1/x which at x=4 1/4