Find given the equation of the line tangent to the graph of at is .

Question

Find  given the equation of the line tangent to the graph of  at  is  . ​

Quizplus · Accepted Answer

The equation of the tangent line to the graph of a function at a point is given by:
y - f(x0) = f'(x0)(x - x0)
where f(x) is the given function, f'(x) is its derivative, and (x0, f(x0)) is the point of tangency.
In this case, we are given that the point of tangency is (11eb0d3b_9842_5e6d_9790_db6cda2c8c47_TB1243_11, 11eb0d3b_9842_5e6e_9790_db128fb0308b_TB1243_11) and the derivative at this point is f'(11eb0d3b_9842_5e6d_9790_db6cda2c8c47_TB1243_11) = 11eb0d3b_9842_5e6b_9790_41647cfd2707_TB1243_11.
Therefore, the equation of the tangent line is:
y - 11eb0d3b_9842_5e6e_9790_db128fb0308b_TB1243_11 = 11eb0d3b_9842_5e6b_9790_41647cfd2707_TB1243_11(x - 11eb0d3b_9842_5e6d_9790_db6cda2c8c47_TB1243_11)
Simplifying and converting to hexadecimal, we get:
y = 11eb0d3b_9842_8580_9790_c5bf8c732ab3_TB1243_11
Therefore, the correct choice is B.

Find Given the Equation of the Line Tangent to the Graph