Question

)Find constants a, b and c, such that the polynomial function f(x) = ax³ + bx² + c will have a local extremum at the point (2, 11) and a point of inflection at (1, 5)

2) A cardboard box with a square base is to have a volume of 8 L. Find the least surface area of the box.
3) Determine all extreme points (local and/or global max/min) for the functions below on the given intervals.
f(x)=3 3√ x^5-15^3 √ x^2,x ∈(1,5) b.f(x)=0.12x/x^2+2x+2, x∈(-2,4)

Answer 1

To have a local extremum at the point (2, 11), the derivative of the function at x = 2 must be zero. Additionally, to have a point of inflection at (1, 5), the second derivative of the function at x = 1 must be zero.