9514 1404 393
Answer:
x = 1
Step-by-step explanation:
The graph of f(x) has a relative minimum where its first derivative (f'(x)) is zero and its second derivative (f''(x)) is positive. (Function f(x) is concave upward when f''(x) > 0.) Since the second derivative is the slope of the first derivative, this means the local minimum will be at the x-value where f'(x) = 0 and is crossing the x-axis from below.
The graph of f'(x) shows a local minimum at x = 1.
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Desmos does not allow us to define f'(x) directly, so we have called it f₁(x). The function f(x) is the integral of that—shown as the dashed orange line. We wanted you to see the f(x) curve so you could see it has a local minimum at x=1.
