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1. is it possible part 2

Is it possible for a function to be defined over the entire real line and to have only one point on the graph where a tangent exists (corrected)
2. Is it possible??

Is it possible for a function to be defined over the entire real line and yet to have no tangents to its graph?
3. Point of Inflection question

Here's an odd one! Define f to be the piecemeal function f(x)=x^2 for x>=0 and f(x) =-(x^2) for x<=0 The graph of f is then sort of like x^3 Does f have a point of inflection at the origin?
4. log question

Quite some time ago there was a question in the two unit paper that involved AP's and stacking logs? It became famous due to the confusion that was generated over the word "log". Does anyone know the year?? Thanks
5. curious perm/com probability question

Here's a strange one! a) A 4 letter word is to be constructed using the 8 characters EEEEEEGG. In how many ways can this be done? b) How many of the words in a) begin and end with an E? c) What is the probability that a 4 letter word constructed from the 8 characters EEEEEEGG begins...
6. A very interesting problem

Here is a spooky little question for everyone preparing for the trials. In how many different ways can six identical black marbles and six idententical white marbles be arranged in a circle? Think carefully abvout your answer
7. Is this true??

Prove that if z ranges over a fixed circle in the complex plane (not containing 0) then the locus of 1/z is also a circle
8. Curly question

Prove that y=x^3 is an increasing function over the entire real line.