an equation for the line tangent to the graph of the differentiable function f at x=3 is y=4x+6. which of the following statements must be true?

If an equation for the line tangent to the graph of the differentiable function f at x=3 is y=4x+6, hence the correct statement out of the given options are statements I and

II.

Given that an equation for the line tangent to the graph of the differentiable function f at x=3 is y=4x+6, in order to know the statement that is true;

If x = 3;

f(3) = 4(3) + 6

f(3) = 12 + 6

f(3) = 18

Hence the statement I is correct

If x = 0

f(0) = 4(0) + 6

f(0) = 0 + 6

f(0) = 6

Hence statement II is correct

From the calculation above, we can conclude that statements I and II are correct.

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B.  I and II only

Step-by-step explanation:

Using the provide information, we are given the equation y = 4x + 6 which is tangent to some function F when x = 3.  Given this, we can say that we can determine the value of our function when x = 0 and when x = 3.  Let's evaluate our functions at these values of x:

X = 0

y = 4x + 6

y = 4(0) + 6

y = 0 + 6

y = 6

X = 3

y = 4x + 6

y = 4(3) + 6

y = 12 + 6

y = 18

Hence, we can agree with the statements I and II.

Cheers.

mr. india