derivatives and tangents ... im stumped? homework help?

Question

Find an equation tangent to the curve ... f(x) = sqrt(5x^2+5x+4) ... at point ... (3,sqrt(64)).

Answer 1

Step 1 :  

The function is and the point is .

The slope of the tangent line is equal to the derivative of the function at .

Apply derivative on each side with respect to x. 

Step 2 :

Slope at the point :

Substitute  in  

The slope is .

Step 3 : 

Point-slope form of line equation

Substitute point and slope in the above equation. 

 

Tangent line equation is 

Solution : 

Tangent line equation is