shown above is the graph of a differentiable function F along with the line tangent to the graph of F at X=3. what is the value of f’3

Tangent lines are lines that touches a curve at a point, without running over the curve.

The value of f'(3) is -1/2

From the figure, the line tangent to the graph passes through (5,3) and (1,5)

Next, we calculate the slope of the line using:

So, we have:

Simplify

Rewrite as:

The line also passes through (3,4) and (1,5)

So, the slope of the line is:

So, we have:

Rewrite as:

The calculated slope is -1/2

This means that:

Substitute

Hence, the value of f'(3) is -1/2

Read more about tangent lines at:

link

Option (A)

Step-by-step explanation:

Function 'f' given in the graph is differentiable with a tangent at x = 3.

Since, slope of the function = value of the differentiated function at a point

Tangent at a point x = 3 is passing through two points (3, 4) and (1, 5).

Slope of the function passing through and is,

Slope =

          =

          =

Therefore, value of f'(3) will be equal to

Option (A) will be the answer.

if you was gonna solve for a, a is a   < -12