Find the function given that the slope of the tangent line to the graph of at any point is and that the graph of passes through the given point.

Question

Find the function  given that the slope of the tangent line to the graph of  at any point  is  and that the graph of  passes through the given point.

Quizplus · Accepted Answer

Since the slope of the tangent line at any point is given, we know that the derivative of the function is constant and equal to 11eaa8b1_dace_b8d9_b1b6_8fbe26385460_TB6026_11. Therefore, the function should be a linear function with a slope of 11eaa8b1_dace_b8d9_b1b6_8fbe26385460_TB6026_11. We can find the y-intercept by plugging in the given point on the graph, which gives us:

11eaa8b1_dace_dfea_b1b6_572379b8903a_TB6026_11 = 11eaa8b1_dace_b8d9_b1b6_8fbe26385460_TB6026_11 * 11eaa8b1_dace_dfeb_b1b6_577a4f2da95e_TB6026_11 + b

Simplifying this, we get:

b = 11eaa8b1_dace_dfea_b1b6_572379b8903a_TB6026_11 - 11eaa8b1_dace_b8d9_b1b6_8fbe26385460_TB6026_11 * 11eaa8b1_dace_dfeb_b1b6_577a4f2da95e_TB6026_11

Therefore, the function is:

11eaa8b1_dace_b8d9_b1b6_8fbe26385460_TB6026_11 * x + (11eaa8b1_dace_dfea_b1b6_572379b8903a_TB6026_11 - 11eaa8b1_dace_b8d9_b1b6_8fbe26385460_TB6026_11 * 11eaa8b1_dace_dfeb_b1b6_577a4f2da95e_TB6026_11)

Simplifying and putting in the given format gives us:

11eaa8b1_dace_dfed_b1b6_656f6a604ce9_TB6026_11

Find the Function Given That the Slope of the Tangent