Final answer:
The provided information is insufficient to determine values for 'a' and 'b' that make a function differentiable, as there is a typo in the question. Clarification of the function is needed for a proper response.
Step-by-step explanation:
The question seems to be related to finding values for constants a and b that will make a given mathematical function differentiable. However, there appears to be a typographical error in the question, and it is unclear what the original function is. Typically, if we're dealing with a polynomial like (x-3)^7, the values of a and b would not affect differentiability, as polynomials are differentiable everywhere. However, without the correct function, we cannot provide specific values for a and b. Additionally, the provided reference information does not seem to directly relate to the question at hand.
If we were to assume the function is based on the quadratic formula, the values of a, b, and c will determine the roots of the function but will not affect whether the function itself is differentiable. The quadratic function is differentiable everywhere. Therefore, to aid in understanding, it would be beneficial to verify the function in question to provide a more accurate and helpful response.
Due to the lack of clarity in the question presented, it is necessary to clarify or correct the original function in order to provide a substantial explanation that would be most beneficial for the student's learning.