Question

Find an equation of the tangent line to the curve at the given point

y = x^3 − 2x + 1, (4, 57)

Answer 1

first find the slope (m), with m = y'(x=4)
so if given y = x^3 − 2x + 1, then y' = 3x^2 - 2.
therefore the slope (m) = 3(4)^2 - 2 = 3(16) - 2 = 48 - 2 = 46

now to form an equation of the tangen line to that curve, use this formula:
y - y1 = m (x - x1)
here x1,y1 = (4,57) and we got m = 46
so,
y - y1 = m (x - x1)
y - 57 = 46 (x - 4)
y - 57 = 46x - 184 or
y = 46x - 184 + 57
y = 46x - 127