Please provide a step by step explanation

d 43. Use the fundamental theorem of calculus (combined with the chain rule) to find f ( t ) dt . dx 2 2 44. Use the definition of the derivative to compute f'(x) given that f (x) = 243- 45. Consider the function f(x) = (x2 - 1)3. (a) State the domain of f and the x and y intercepts. (b) Specify any symmetry. (c) State the open intervals where f is increasing and where it is decreasing. (d) State the critical numbers of f and classify each as a local minimum, local maximum, or neither (e) Sketch the graph of f