Final answer:
The student's question concerns calculus and the properties of a function based on its derivative, f'(x) = sin(x³). Specific work requires the complete interval. Calculus, trigonometric function behavior, integration, and differentiation are key concepts involved.
Step-by-step explanation:
A student has asked about the function f with its first derivative defined by f'(x)=sin(x³) on the interval [-1.8, ?]. Unfortunately, a part of the question regarding the upper limit of the interval seems to be missing or unclear. To provide a specific answer, we would need the complete interval. Regardless, the question is mathematical, specifically concerning calculus, as it involves finding information about a function given its derivative. Derivatives play a critical role in calculus as they represent the rate of change of functions and are used to determine slopes of tangent lines, motions, and other rates.
To proceed with such a problem, normally one would evaluate the behavior of f'(x) on the defined interval to understand where the function f(x) is increasing or decreasing, and to find local extrema. If finding the function f(x) itself is necessary, one would need to integrate f'(x). The sine function oscillates between -1 and +1, which means f'(x) will also oscillate, causing f(x) to have points of inflection corresponding to where f'(x) crosses zero. It's essential to understand how to interpret the derivatives and use the integration to piece together the behavior of the original function.
Given the context of the question, it seems to expect the student to utilize knowledge of trigonometric functions and their properties, along with skills in differentiation and integration from calculus. Additionally, understanding how to analyze the derivative graphically and algebraically to infer the properties of the original function is implied.