Find an equation of the tangent line to the curve at the given point. y = 3x3 - x2 + 2, (1, 4)

y = 7x - 3

Note the gradient of the tangent is the derivative of y at x = 1

Differentiate using the power rule

(a) = na

y = 3x³ - x² + 2

= 9x² - 2x

x = 1 : = 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

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