Question 992048
f(x) = 3x^2 -11x + +23
f'(x) is the first derivative of f(x)
f'(x) = 6x -11
f'(x) gives us the slope of the tangent line at any x on f(x)
we are given the point (1,15), therefore
slope of tangent line at x = 1 is f'(1) = 6 - 11 = -5
so far we have
y = -5x + b
but we are given the point (1,15)
15 = -5 + b
b = 20
therefore the equation of the line tangent to f(x) at (1,15) is
y = -5x + 20