EXAMPLE 5.2(a) Find the slope of the tangent to the curveyr-3z+2 at th

1.	EXAMPLE 5.2(a) Find the slope of the tangent to the curveyr-3z+2 at the point whose z-co-ordinate is3.(b) Find the equation of the tangent to the curve+4z+1 at the point whose z co-ordinate is 3.
Answer» a)slope of tangent = y' = 3x²-3 and the Vale at x = 3 is = dy/dx = 3(3)²-3 = 24. b) y = x²+4x+1 , slope at x = 3 is y' = 2x+4 = 2(3)+4 = 10 =m and y = (3)²+4(3)+1 = 22 so, equation of line of tangent is y = mx+c=> y = 10x+C .. putting (3,22) in the line=> 22 = 10*3 +C => C = -8 so, equation is y = 10x-8

EXAMPLE 5.2(a) Find the slope of the tangent to the curveyr-3z+2 at the point whose z-co-ordinate is3.(b) Find the equation of the tangent to the curve+4z+1 at the point whose z co-ordinate is 3.

Answer»

a)slope of tangent = y' = 3x²-3 and the Vale at x = 3 is = dy/dx = 3(3)²-3 = 24.

b) y = x²+4x+1 , slope at x = 3 is

y' = 2x+4 = 2(3)+4 = 10 =m

and y = (3)²+4(3)+1 = 22

so, equation of line of tangent is y = mx+c=> y = 10x+C .. putting (3,22) in the line=> 22 = 10*3 +C => C = -8

so, equation is y = 10x-8