Worksheet: Tangents to the Graph of a Function

Find the equation of the tangent to the curve at .

Find the equation of the tangent to the curve at .

Find the equation of the tangent to the curve at .

If the line is tangent to the graph of the function at , what is ?

If the line is tangent to the graph of the function at , what is ?

What is the -coordinate of the point where the tangent line to is parallel to the -axis?

What is the -coordinate of the point where the tangent line to is parallel to the -axis?

The point lies on the curve . If the gradient of the tangent there is , what are the values of constants and ?

The point lies on the curve . If the gradient of the tangent there is , what are the values of constants and ?

Find the equation of the tangent to the curve that makes an angle of with the positive -axis.

Suppose the line touches the curve . What is ?

If the curve is tangent to the line at , find the constants and .

Find the point on the curve at which the tangent to the curve is parallel to the -axis.

The line touches the curve at . Find and .

Do the curves and meet at a common tangent? If so, give the equation of this tangent.

Determine the equation of the line tangent to the curve at point .

The line is tangent to the curve at the point . Find , , and .

The line is tangent to the graph of function at the point . What is ?

The line touches the curve at the point . Find and .

Find the equation of the tangent to the curve at the point on the curve.

Find the gradient of the tangent to the curve when , approximated to the nearest hundredth, if needed.

Find the equation of the tangent to the curve at the point .

Find the equation of the tangent to the curve at the point .

List the equations of all the tangents to that also lie on the point .

List the equations of all the tangents to that also lie on the point .