Question

Need help with derivative?

The tangent line to the graph of a function f at the point x=7 is y=5x−34. Find the tangent line to the graph of y=xf(x) at x=7. Put your answer into slope-intercept form.

 

 

Answer 1

Step 1 :

Tangent line equation is .

At , .

Tangent line equation is .

Differentiate the above equation with respect to .

.

Step 2 :

The curve equation is .

Considering the function as .

Differentiate the curve with respect to .

.

Evaluating at .

.

.

Derivative of the function is the slope of the tangent line.

The tangent line to the graph at is the line with slope 36 and passing through the point .

Point-slope form of a line equation is .

Let the point is and the slope is .

Substitute the corresponding values in point-slope form.

The tangent line equation is .

Solution :

The tangent line equation is .