Question

(1)Suppose that the DERIVATIVE of R(X) ( i.e., R PRIME OF X) ) equals:
R’(X) =[ 5*(X^3) ] - [ 60 * (X^2) ]
(A)   Please determine TWO HYPERCRITICAL NUMBERS FOR X.
( i.e., solve the equation: R’’(X)=0 )
(B)   Please TEST EACH hypercritical number, to VERIFY that EACH hypercritical number corresponds to an INFLECTION POINT; HERE IS HOW YOU SHOULD DO SO:
You must determine ONLY THE SIGN of the SECOND DERIVATIVE, TWO TIMES PER HYPERCRITICAL NUMBER :
FIRST, you evaluate R’’(X) at a value of X which is SLIGHTLY LOWER THAN the hypercritical number; SECOND, you evaluate R’’(X) at a value of X which is SLIGHTLY HIGHER THAN the hypercritical number; please VERIFY that , for EACH hypercritical number, the TWO signs of R’’(X) are DIFFERENT !!

Answer 1

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