musad said:I am having trouble getting started with this question.
Suppose that f(4)=7 and f′(4)=−2. Use the product rule to find the derivative of xf(x) when x=4. Thanks
The derivative of xf(x) at x=4 is -2. This means that the slope of the tangent line at x=4 is -2.
To find the derivative of xf(x) at x=4, you can use the power rule. First, multiply the coefficient (x) by the exponent (1) to get 1x. Then, subtract 1 from the exponent to get 0. Finally, the derivative is the coefficient (1) multiplied by the new exponent (0), which is 1*0=0. Therefore, the derivative of xf(x) at x=4 is 0.
A derivative of -2 means that the slope of the tangent line at x=4 is -2. This means that the function f(x) is decreasing at x=4, since the slope is negative.
The derivative of a function f(x) at a specific point x is the instantaneous rate of change of the function at that point. In other words, it represents the slope of the tangent line at that point. Therefore, the derivative of xf(x) at x=4 is a way to describe the slope of the original function at x=4.
Yes, you can graph the derivative of xf(x) at x=4 by plotting a point at (4,-2) on a coordinate plane. This point represents the slope of the tangent line at x=4. You can also graph the original function f(x) and see how the slope changes at x=4.