Final answer:
To sketch the graph of a continuous function on the interval [-2,4] with f'(-1)=f'(0)=0, plot the points (-2,4), (-1,1), (0,0), (1,1), and (4,16) and connect them with a smooth curved line. The function f(x) = x^2 satisfies the given conditions.
Step-by-step explanation:
To sketch the graph of a continuous function on the interval [-2,4] with the given properties, we can start by using the information that f'(−1)=f'(0)=0. This means that the function has horizontal tangents at x=-1 and x=0. We can choose a simple function that satisfies these conditions, such as f(x) = x^2.
Plotting the points (-2,4), (-1,1), (0,0), (1,1), and (4,16), and connecting them with a smooth curved line, we obtain the graph of the function f(x) = x^2 on the interval [-2,4].