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- YOUR TURN Find an equation of the curve whose tangent line has slope f(x)=3x1/2+4 and passes through the point (1,2).Explain the relationship between the slope and the derivative of fx at x=a.Write an equation for z' if z(x) = 3x2 + 5x + 1. Then, write the equation of the tangent line in point slope form at x = -2.
- Find an equation for the line perpendicular to the tangent line to the curve y = x3 - 4x + 1 at the point (2, 1)If f(x) = 3x² - 2x + 7, find f'(-2). = Use this to find the equation of the tangent line to the parabola y 3x²2x + 7 at the point (-2, 23). The equation of this tangent line can be written in the form y = mx + b where m is: and where b is:Calculate the second and third derivatives. y" = y"" = G 9- y = 7x²¹ - 7x² + 9x
- find the slope of y=x^2-2x-5 at the point (2,-5) The equation of the tangent line to the curve at P(2,−5) isFind the equations for the two distinct tangent lines to the curve y= x^2 that pass through the point (-1, -3).Find the equation of the line tangent to the curve xy^3+xy=6 at the point (3,1). When the equation of this tangent line is written in the form y=mx+b.
- Find the equation of the line tangent to the curve (x-2)^2=-4(y+3) at (2,-3)If f(x) = 4x² - 4x + 2, find f'(-3). Use this to find the equation of the tangent line to the parabola 4x² - 4x + 2 where x = The equation of this tangent line is | Y = 3.Find the slope and equation of the tangent line to the curve y = x3 + 2x + 1 at ( 2,4)