Optimisation Problems

Given a function g(x), if g'(x)=0 at a certain value of x, then g(x) has _____________ at x.

• an inflection point

• a stationary point

• a minimum

• a maximum

For a function g(x), g'(-2)=0 indicates that x=-2 is ________________.

• an inflection point

• a stationary point

• a relative maximum

• a relative minimum

The gradient of a function is given by its ____________.

• first derivative

• second derivative

• third derivative

• expression

We want to construct a box whose base length is 3 times the base width. If the box must have a volume of 50 ft³, determine the dimensions that will minimize the amount of material used.

• w=2.027ft, h=4.055ft, l=6.082ft
• w=1.488ft, h=3.347ft, l=6.694ft
• w=2.231ft, h=3.347ft, l=6.694ft
• w=0.485ft, h=2.111ft, l=4.222ft

If y=2x-8, what is the minimum value of the product xy?

• -16
• -8
• -4
• 2

If f '(x) changes from negative to positive, then f(x) has __________ at x.

• a maximum

• a minimum

• no extrema

The normal to the curve is 

• the derivative
• the integral
• perpendicular to the tangent  to the curve
• the tangent to the curve