Question

1. Let u(x) and v(x) be functions such that

u(1)=2,u′(1)=3,v(1)=6,v′(1)=−1

If f(x)=u(x)v(x), what is f′(1). Explain how you arrive at your answer.

2. If f(x) is a function such that f(5)=9 and f′(5)=−4, what is the equation of the tangent line to the graph of y=f(x) at the point x=5? Explain how you arrive at your answer.

3. Find the equation of the tangent line to the function g(x)=xx−2 at the point (3,3). Explain how you arrive at your answer.

4. The position of an object moving along a coordinate line is given by s(t)=306−t. Find the object's speed and acceleration at time t=5. Explain how you arrive at your answer.

Answer 1