The writer must be conscious of the separateness that exists between himself and his reader. The reader's only access to the mind of the writer is through the words on the page.

## GRE Math Practice Test Problems

### By Maurice Ticas

Studying for the exam I've encountered two problems. The first is stated as follows:

If $$f$$ is a continuously differentiable real-valued function defined on the open interval $$(-1,4)$$ such that $$f(3)=5$$ and $$f'(x)\geq-1$$ for all $$x$$, what's the greatest value of $$f(0)$$?

The second I thought was difficult too and worth sharing:

Suppose $$g$$ is a continuous real-valued function such that $$3x^5+96=\int_c^x g(t) dt$$ for each $$x \in \mathbb{R}$$, where $$c$$ is a constant. What is the value of $$c$$?

What approach do you have to answer the two problems?