Thread: Equation of line that is tangent to graph of f and parallel

I need to find an equation of the line that is tangent to the graph and parallel to the given line:

function:


line:


How can I do this problem? (step by step always works best for me )

Thanks so much for reading!!

Good day AMaccy. Step by step it is then

Step 1. Rearrange the line equation into the form y=mx+c


Step 2. Remember that your teacher said,for our line to be parallel to the given line, it must have the same gradient.

Step 3. Gain insight/remember for a line to be tangent to a curve, it must possess the same gradient as the curve at one particular point.

Step 4. Knowing these 2 facts, we state that the gradient of our wanted line is
Step 5. Differentiate the curve to discover where it's gradient is
, Let

Step 6. Obtain the y-coordinate at x=



Step 7. We now have the point at which the curve and line touch and our line's gradient, calculate our line's y-intercept.




So the equation of the line is

Originally Posted by AMaccy

I need to find an equation of the line that is tangent to the graph and parallel to the given line:

function:


line:


How can I do this problem? (step by step always works best for me )

Thanks so much for reading!!

1. Re-write the equation of the line:

. Thus the slope is

2. The slope of the tangent equals first derivation of f at the tangent point. Therefore you need the first derivation:



Solve for x: m = f'(x):


The tangent point has the coordinates because T is a point of the graph of f.

3. Use the point-slope-formula to get the equation of the tangent:

Solve for y:

"British English", "gradient".
"American English", "slope". Both mean the same thing.