Question

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

Answer 1

y = 7x - 3

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

Differentiate using the power rule

$\frac{d}{dx}$(a$x^{n}$) = na$x^{n-1}$

y = 3x³ - x² + 2

$\frac{dy}{dx}$ = 9x² - 2x

x = 1 : $\frac{dy}{dx}$ = 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