Question

find k such that the line is tangent to the graph

Answer 1

Step 1:

The function is and the tangent line is .

Compare the tangent line with slope-intercept form of line equation ,

where is the slope and is the -intercept.

Slope of the tangent line is .

Step 2:

The function is .

Apply derivative on each side.

Slope of the tangent line is .

But slope of the tangent line is .

Step 3:

Substitute the value of in the function.

.

Equate and .

Substitute in .

Solution:

The value of is 3.