Resumen de Monotonicity and logarithmic concavity of two functions involving exponential function

Ai-Qi Liu, Guo-Fu Li, Feng Qi

• The function [image omitted] for x?>?0 is proved to be strictly decreasing. As an application of this monotonicity, the logarithmic concavity of the function [image omitted] for a???? and t???(0,?8) is verified. The possible origin and background of the function (*) are revealed to be related to [image omitted] the remainder of Binet's formula. Some applications of above results to the difference of ?(x) are notedThis study investigated the effects of self and cooperative-instructional strategies on senior secondary school students' attitude towards Mathematics. The moderating effects of locus of control and gender were also investigated. The study adopted pre-test and post-test, control group quasi-experimental design using a 3 ?×?2 ?×?2 factorial matrix with two experimental groups and one control group. Three hundred and fifty SSS II students from six purposively selected secondary schools in Ijebu-North Local Government Area of Ogun State were the subjects. Three instruments were developed, validated and used for data collection. Analysis of Covariance (ANCOVA) and Scheffe post hoc analysis were the statistics used for data analysis. Findings showed that the treatments had significant main effect on students' attitude towards Mathematics. The participants exposed to self-instructional strategy had the highest post-test mean attitude score. The study found no significant main effects of locus of control and gender on the participants' attitude towards Mathematics. It was concluded that Mathematics teachers should be trained to use self and cooperative learning packages in the classroom, since the strategies are more effective in improving students' attitude towards Mathematics than the conventional method.