(a) State the analytical condition involving the first derivative that guarantees a…
MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
(a) State the analytical condition involving the first derivative that guarantees a differentiable function is strictly decreasing on an interval.
(b) For the polynomial function f(x)=x4+kx2+1, examine the possibility of choosing a real parameter k so that f is strictly decreasing on the entire real line. Give a reasoned argument to support your conclusion without producing a complete sign table.