Optimisation and curve sketching
38 problems · Extrema and the study of functions.
Ex.15A fence along a river
Optimisation and curve sketching
High school
Ex.86How many trees in the orchard?
Optimisation and curve sketching
High school
Ex.109Distance to a line, without a formula
Optimisation and curve sketching
High school
Ex.116Least squares for a line through the origin
Optimisation and curve sketching
L1
Ex.121The most economical speed of a truck
Optimisation and curve sketching
High school
Ex.123The economic order quantity
Optimisation and curve sketching
L1
Ex.125Maximising profit
Optimisation and curve sketching
L1
Ex.127The strongest beam cut from a log
Optimisation and curve sketching
L1
Ex.129A window with a semicircular top
Optimisation and curve sketching
L1
Ex.132The trapezoid of largest area with three equal sides
Optimisation and curve sketching
L1
Ex.135The triangle of least area through a point
Optimisation and curve sketching
L1
Ex.137Among triangles with a given base and perimeter, the isosceles one is the largest
Optimisation and curve sketching
L2
Ex.139The largest rectangle inscribed in an ellipse
Optimisation and curve sketching
L1
Ex.141The largest cone and the largest cylinder inscribed in a sphere
Optimisation and curve sketching
L1
Ex.142The paper cup of largest capacity
Optimisation and curve sketching
L1
Ex.144At which height should a lamp be hung?
Optimisation and curve sketching
L2
Ex.147Maximum sustainable yield
Optimisation and curve sketching
L2
Ex.149The shortest path touching a line
Optimisation and curve sketching
L1
Ex.152The closest point of an ellipse
Optimisation and curve sketching
L1
Ex.154Minimising a/x + b/(1 − x)
Optimisation and curve sketching
L2
Ex.156The best constant approximating x²
Optimisation and curve sketching
L2
Ex.158Firing up a slope: the best angle
Optimisation and curve sketching
L2
Ex.159The maximum of 3 sin x + 4 cos x
Optimisation and curve sketching
L1
Ex.161Global extrema of x³ − 3x on [−2, 3]
Optimisation and curve sketching
High school
Ex.163Extrema of |x² − 3x + 2| on [0, 3]
Optimisation and curve sketching
High school
Ex.167The maximum of xⁿe^(−x)
Optimisation and curve sketching
L1
Ex.168The minimum of x^x
Optimisation and curve sketching
L1
Ex.171A family of functions: x² + m/x
Optimisation and curve sketching
L1
Ex.172Complete study of x e^(−x)
Optimisation and curve sketching
L1
Ex.175Complete study of (ln x)/x
Optimisation and curve sketching
L1
Ex.176Sketching x³/(x² − 1)
Optimisation and curve sketching
L2
Ex.177Sketching x√(1 − x²)
Optimisation and curve sketching
L2
Ex.178How many solutions does eˣ = ax have?
Optimisation and curve sketching
L1
Ex.395The largest rectangle in a semicircle
Optimisation and curve sketching
High school
Ex.396The most economical can
Optimisation and curve sketching
High school
Ex.755Which is larger, e^π or π^e?
Optimisation and curve sketching
L1
Ex.782The closest point on a parabola
Optimisation and curve sketching
L1
Ex.1513The longest ladder around a corner
Optimisation and curve sketching
L2
No problem matches these filters.