Question

Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm year results. (If an answer is undefined, enter UNDEFINED. Round your answer to three decimal places.) f′(5)=xf(x)=(x2−4x)24(5,4/25)

Answer 1

To find the slope of the graph at a given point, you need to find the derivative of the function and evaluate it at that point. In this case, the derivative of the function x^2 - 4x / 24 is 1/3, so the slope of the graph at (5, 4/25) is 1/3.

Step-by-step explanation:

The slope of a curve at a point is equal to the slope of a straight line tangent to the curve at that point. To find the slope of the graph of the function at the given point (5, 4/25), we need to find the derivative of the function and evaluate it at x = 5. The derivative of the function x^2 - 4x / 24 is obtained by applying the power rule and the constant rule of differentiation. The derivative is 1/3, so the slope of the graph at the given point is 1/3.