Question

f(x)=x√x²+9 defined on the interval −5≤x≤6. f(x) is concave down on the interval x= ___________ to x= ___________.

Answer 1

To find when the function f(x)=x√(x²+9) is concave down, calculate its second derivative and look for intervals where this derivative is negative.

Step-by-step explanation:

The question is asking to determine the interval where the function f(x)=x√(x²+9) is concave down. To solve this, we need to find the second derivative of the function and find where it is negative, as this indicates concavity downward.

First, compute the first derivative (f'(x)) using the chain rule and product rule. Next, compute the second derivative (f''(x)) from the first derivative. The second derivative will be a function of x. Then, find the values of x where f''(x) is negative, as these will be the intervals where the graph of f(x) is concave down.

Note that this involves advanced calculus concepts such as differentiation and analysis of concavity, which might not be fully covered in this response.