Question

Given that
f(x)=2250/(x+7)
What is the slope of the tangent line to f(x) when x=10.

Answer 1

Approximately -7.79.

Step-by-step explanation:

To find the slope of the tangent line to f(x) when x = 10, we need to compute the derivative of f(x) and evaluate it at x = 10.

Given f(x) = 2250 / (x + 7), we can find the derivative using the quotient rule. The quotient rule states that for a function f(x) = u(x) / v(x), the derivative f'(x) is given by:

f'(x) = (u'(x) * v(x) - u(x) * v'(x)) / (v(x))^2

In this case, u(x) = 2250 and v(x) = (x + 7), So:

f'(x) = [(0 * (x + 7)) - (2250 * 1)] / ((x + 7)^2)

= (-2250) / (x + 7)^2

Evaluate f'(x) at x = 10:

f'(10) = (-2250) / (10 + 7)^2

= (-2250) / (17)^2

= (-2250) / 289

≈ -7.79

Therefore, the slope of the tangent line to f(x) when x = 10 is approximately -7.79.

Answer 2

The slope of the tangent line to f(x) when x=10 is approximately -7.791.

Step-by-step explanation:

To find the slope of the tangent line to f(x) when x=10, we need to find the derivative of f(x) with respect to x and then evaluate it at x=10. The derivative of f(x) is found using the quotient rule, which states that if f(x) = u(x)/v(x), then f'(x) = (u'(x)v(x) - u(x)v'(x)) / (v(x))^2. In this case, u(x) = 2250 and v(x) = x+7.

Applying the quotient rule, we have f'(x) = (0*(x+7) - 2250*1) / ((x+7)^2) = -2250 / (x+7)^2.

Now, we can substitute x=10 into f'(x) to find the slope of the tangent line at x=10:

f'(10) = -2250 / (10+7)^2 = -2250 / 289 = -7.791.