Question

(a) Find the slope m of the tangent to the curve y = 2 + 4x² − 2x³ at the point where x = a.
m =  

(b) Find equations of the tangent lines at the points (1, 4) and (2, 2).

y(x)	=	(at the point (1, 4))
y(x)	=	(at the point (2, 2))

(c) Graph the curve and both tangents on a common screen.

say and the sose m of the target to the survey * 2 * * - 20 ste se (a) Find the slope m of the tangent to the curve y = 2 + 4x2 – 2x3 at the point where x = a. m = (b) Find equations of the tangent lines at the points (1, 4) and (2, 2). y(x) = (at the point (1, 4)) y(x) = (at the point (2, 2)) (c) Graph the curve and both tangents on a common screen.

Answer 1

y = 2+422 223 slope in of tangent is given by the derivative clue = m = 4(22) – 2(372) m=8x-6x² . At a=a, slope is: m= 8a-6a? Tangent at (1,4): m = 8(1)-6112 m= 2 (Slope of tangent) {quation of tangent a straight line : (y-yo)= m (x-ko) y-4 = 2(2-1). y = 206+ 2 * [Egustion of tangent "at (1,4)] Tangent at : (2,2) m = 8(2) - 6(2) = 16 – 24 = -8 (y - Yo) = m (2-40) - [Semanal equation of a sheight -2=-8(2-2) y = - 8x + 18 * [Equation of tangent at (3,2)

To draw Page Core the twitt curve. y = 2 + 42² - 223 dy = 82-622 - dy=0 at x=0 and a & x=4 3 7=0 x= e function decreases from to e 6-00,0)ulco and increases in (0.4) minima occurs at q=0 a local marina at w= local a thus and ادرا)

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