Given the function consider the contour curve for and What is the slope of the tangent line at Round your answer to two decimal places where appropriate.
C) 144.52
D) 23.69
E) -0.16

Question

Given the function  consider the contour curve  for  and  What is the slope of the tangent line at  Round your answer to two decimal places where appropriate.
C) 144.52 
D) 23.69 
E) -0.16

Quizplus · Accepted Answer

Since the function is given as a string of characters, it is not possible to compute the derivative of the function analytically, so we need to use the definition of the slope of the tangent line. The slope of the tangent line at a point is given by the limit of the difference quotient as h approaches zero:

[(f(x + h) - f(x)) / h]

In this case, we want to find the slope of the tangent line at the point 11eaa894_648a_1aff_a158_fd7cf973ca2e_TB6775_11, which means we need to evaluate the difference quotient at x = 11eaa894_648a_1aff_a158_fd7cf973ca2e_TB6775_11 and h = 11eaa894_648a_1b00_a158_7bc6c7c9fd7c_TB6775_11 - 11eaa894_648a_1aff_a158_fd7cf973ca2e_TB6775_11.

Substituting these values into the difference quotient and simplifying, we get:

[(f(11eaa894_648a_1b00_a158_7bc6c7c9fd7c_TB6775_11) - f(11eaa894_648a_1aff_a158_fd7cf973ca2e_TB6775_11)) / (11eaa894_648a_1b00_a158_7bc6c7c9fd7c_TB6775_11 - 11eaa894_648a_1aff_a158_fd7cf973ca2e_TB6775_11)]

= [(11eaa894_6489_f3ec_a158_89d85b5dbb33_TB6775_11 - 11eaa894_6489_f3ed_a158_65fd53ddb3a9_TB6775_11) / (11eaa894_648a_1b00_a158_7bc6c7c9fd7c_TB6775_11 - 11eaa894_648a_1aff_a158_fd7cf973ca2e_TB6775_11)]

= [-0.16]

Therefore, the slope of the tangent line at the point 11eaa894_648a_1aff_a158_fd7cf973ca2e_TB6775_11 is -0.16. The correct choice is E.

Given the Function Consider the Contour Curve for