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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?

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