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

f(x) = √x - x; f(4) = √4 - 4 = - 2; f'(x) = 1/2x^-1/2 - 1; f(4) = 1/2·4^-1/2 - 1 = 1/4 - 1 = - 3/4;

So, equation of tangent line y = - 2 - 3/4(x - 4) or y + 2 = -3/4(x - 4).

Answer: a)