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

to find the perimeter of the rectangle this is the expression:

x-9+x-9+3x-4+3x-4=138

if we simplify it:

8x-26=138

remember, 138 is what it all adds up to

the length is 11.5cm

the width is 57.5cm

the area is 661.25cm^2

the answers might not be correct use at own risk