Find the slope of the tangent line to the graph of the function at the given point. fix) = 14 at (1, 14) 5x 5 e Determine an equation of the tangent line. Step - 1 We have given graph of function at the point f (x ) = 14 at (1 , 14 5x so , 9 = 14 SX We know the slope of curve at point (x, 4) find first- derivative dy a 14 dx dx 5 0C 14 d S dx ( ) - - 14 5 x2 dy 14 so 2 step - 2 use the point Given to find the slope m = - 14 Where X= 1 5 given point-3 50( 2 - 14 S( 172 m 2 - 14Step - 3 Now we have slope of tangent - line and a point- from where live goes through m = 14 ( x , , 4 , ) = ( 1 1 14 ) Equation of line formula when slope and one point given. Y - Y , = m ( X - x 1 ) step - 4 Put values in formula y - 14 5 14 ( x - 1 ) y - 14 - 14 X + 14 y = 14 X + + 5 =) Y = - 14 x + 28 5 Equation of target line