Question

Part 1: The derivative at a specific point Use the definition of the derivative to compute the derivative of f(x) = 7/x at the specific point x = 2. Evaluate the limit by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box). f'(2) = lim_{h?0} ( (f(2 + h) - f(2)) / h ) = lim_{h?0} ( ? ) = ? Part 2: The derivative function Use the definition of the derivative to compute the derivative of the function f(x) = 7/x at an arbitrary point x. Evaluate the limit by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box). f'(x) = lim_{h?0} ( (f(x + h) - f(x)) / h ) = lim_{h?0} ( ? ) = ? Part 3: The tangent line Now let's calculate the tangent line to the function f(x) = 7/x at x = 7. a. By using f'(x) from part 2, the slope of the tangent line to f at x = 7 is f'(7) = ?. b. The tangent line to f at x = 7 passes through the point (7, f(7)) = ? on the graph of f. (Enter a point in the form (2, 3) including the parentheses.) c. An equation for the tangent line to f at x = 7 is y = ?.

          Part 1: The derivative at a specific point
Use the definition of the derivative to compute the derivative of f(x) = 7/x at the specific point x = 2. Evaluate the limit by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box).
f'(2) = lim_{h?0} ( (f(2 + h) - f(2)) / h ) = lim_{h?0} ( ? ) = ?
Part 2: The derivative function
Use the definition of the derivative to compute the derivative of the function f(x) = 7/x at an arbitrary point x. Evaluate the limit by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box).
f'(x) = lim_{h?0} ( (f(x + h) - f(x)) / h ) = lim_{h?0} ( ? ) = ?
Part 3: The tangent line
Now let's calculate the tangent line to the function f(x) = 7/x at x = 7.
a. By using f'(x) from part 2, the slope of the tangent line to f at x = 7 is f'(7) = ?.
b. The tangent line to f at x = 7 passes through the point (7, f(7)) = ? on the graph of f. (Enter a point in the form (2, 3) including the parentheses.)
c. An equation for the tangent line to f at x = 7 is y = ?.

Part 1: The derivative at a specific point
Use the definition of the derivative to compute the derivative of f(x) = 7/x at the specific point x = 2. Evaluate the limit by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box).
f'(2) = limh?0 ( (f(2 + h) - f(2)) / h ) = limh?0 ( ? ) = ?
Part 2: The derivative function
Use the definition of the derivative to compute the derivative of the function f(x) = 7/x at an arbitrary point x. Evaluate the limit by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box).
f'(x) = limh?0 ( (f(x + h) - f(x)) / h ) = limh?0 ( ? ) = ?
Part 3: The tangent line
Now let's calculate the tangent line to the function f(x) = 7/x at x = 7.
a. By using f'(x) from part 2, the slope of the tangent line to f at x = 7 is f'(7) = ?.
b. The tangent line to f at x = 7 passes through the point (7, f(7)) = ? on the graph of f. (Enter a point in the form (2, 3) including the parentheses.)
c. An equation for the tangent line to f at x = 7 is y = ?.

Added by Jose D.

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