If the instantaneous rate of change of g(x) at is , write the equation of the line tangent to the graph of g(x) at
A)x = - Y +
B)x = Y +
C)x = Y -
D)y = X -
E)y = X +

Question

If the instantaneous rate of change of g(x) at  is  , write the equation of the line tangent to the graph of g(x) at  ​
A)x = - Y + 
B)x = Y + 
C)x = Y - 
D)y = X - 
E)y = X +

Quizplus · Accepted Answer

The equation of the tangent line at a point (a, g(a)) is given by y - g(a) = g'(a)(x - a). Therefore, using the given instantaneous rate of change of g(x) at 11eb0d3b_9842_ac94_9790_713b8dc7ed03_TB1243_11 , we get the equation of the tangent line as y - 11eb0d3b_9842_d3ad_9790_c9d15ce37630_TB1243_11 = 11eb0d3b_9842_ac95_9790_87a958b1cfd9_TB1243_11 (x - 11eb0d3b_9842_d3ad_9790_c9d15ce37630_TB1243_11), which can be rearranged as y = 11eb0d3b_9842_d3ad_9790_c9d15ce37630_TB1243_11 (x - 11eb0d3b_9842_d3ae_9790_8b15db8a09eb_TB1243_11) + 11eb0d3b_9842_d3ad_9790_c9d15ce37630_TB1243_11. This matches option D.

If the Instantaneous Rate of Change of G(x) at