Chapter 6 – Application of Derivatives

1. What does f′(x)>0 indicate about f(x)?

2. What does f′(x)<0 indicate?

3. State the first derivative condition for a local maximum.

4. State the first derivative condition for a local minimum.

5. Find the critical point of f(x)=x²−4x+3.

6. What is the geometrical meaning of f′(x)?

1. Find the intervals in which f(x)=x²−6x+5 is increasing or decreasing.

2. Find the critical points of f(x)=x³−3x².

3. Determine whether x=0 is a maximum or minimum for f(x)=x².

1. Find the maximum and minimum values of x+1/x for x>0.

2. Find the equation of the tangent to y=x² at x=2 and interpret its slope.

3. Find the dimensions of a rectangle of maximum area having perimeter 40 units.

1. A rectangular sheet has perimeter 60 cm. Using derivatives, determine its dimensions for maximum area and prove that the result gives a maximum.