y = 7x - 3
Note the gradient of the tangent is the derivative of y at x = 1
Differentiate using the power rule
[tex]\frac{d}{dx}[/tex](a[tex]x^{n}[/tex]) = na[tex]x^{n-1}[/tex]
y = 3x³ - x² + 2
[tex]\frac{dy}{dx}[/tex] = 9x² - 2x
x = 1 : [tex]\frac{dy}{dx}[/tex] = 9 - 2 = 7 ← gradient of tangent
equation in point- slope form, using m = 7 and (a, b) = (1, 4)
y - 4 = 7(x - 1) ← point-slope form
y - 4 = 7x - 7
y = 7x - 3 ← in slope-intercept form
