Find the equation of the tangent line to the function fx 3x

Find the equation of the tangent line to the function f(x) = 3xx at x = 3.7 What is the y-intercept of the tangent line equation that you found ?

f(x) = 3xx = 3x^2 at x = 3.7

f( 3.7) = 3(3.7)^2 = 41.07

Now we find the derivative of f(x), df/dx to find the slope of the line df/dx = 6x

Slope m = 6x at x= 3.7 = 22.2

Now stad equation ofline : y =mx+c ----> y = 22.2x +c

Let find c using ( 3.7 , 41.07)

41.07 = 22.2*3.7 +c

c= -41.07

Equation of Line: y = 22.2x -41.07

Y intercept y = -41.07