Let f(x)=x^2+8x, find the slope of the secant line joining (1,f(1)) and (8,f(8)), find the slope of the secant line joining (6,f(6)) and (6+h,f(6+h)), Find the slope of the tangent line at (6,f(6)),

Question

Find the equation of the tangent line at (6,f(6))

Answer 1

f(x) = x^2 + 8x

f(1) = 1+8= 9

f(8) = 64+64 = 128

the secant line from (1,9) to (8,128) has slope = (128-9)/(8-1) = 119/7= 17

slope = 17

slope of the tangent line at (6,f(6))=(6,36+48) = (6,84) is f'(6) = 2x+8 = 2(6)+8 = 20