Find the function f given that the slope of the tangent line to the graph of f at any point is and that the graph passes through the point (0, 6).
B)
C)
D)
E)

Question

Find the function f given that the slope of the tangent line to the graph of f at any point  is  and that the graph passes through the point (0, 6). ​
B) ​ 
C) ​ 
D) ​ 
E) ​

Quizplus · Accepted Answer

Since the slope of the tangent line at any point x is given by f'(x), we know that f'(x) = 11eb651f_cb03_fe2f_b0a1_19a7c2830ad5_TB8255_11 for all x. Thus, we can integrate this to find f(x). Using the initial condition f(0) = 6, we get:

f(x) = 11eb651f_cb04_2542_b0a1_a1e610acac14_TB8255_11x + 6

Therefore, choice C is the correct answer.

Find the Function F Given That the Slope of the Tangent