Find the equation of the tangent line to the curve f (a) = -2x2 - 1 at x = 0. O T(ac) = 1 O T(ac) = 0 O T(a) = -1 O T(a) = -20Find the equation of the tangent line to the curve f(a ) = ac2 - 2x + 1 at x = 0. O T(a) = 0+(-2) (2-0) O T(a) = 1+ (-2)(2-0) O T(a) = 0+ (2) (2 - 0) O T(a) = 1+ (2) (x -0)Find the equation of the tangent line to the curve f(x) = sin(x). Assume f '(x) = cos(x) at x = TT N O T(X) = -1 O T(a ) = O T( X ) = 0 O T(X) = 1Find the equation of the tangent line to the curve f( x ) = Assume f'( x ) and x = 1. O T(X) = 1 - (X- 1) O T(X) = 1 + (x - 1) O T(X) = (X- 1) O T() =-(x - 1)A differentiable function has the value y(5) = 1 and the derivative value y'(5) = -7. Approximate the value of y(5.2). O 5.2 0 0.4 O -0.4 O -7.2A differentiable function has the value y(2) = 3 and the derivative value y'(2) = -5. Approximate the value of y(1.9). O 3.5 0 3 O 2 O 1.9\f2 cos inverse x find f xFind the equation of the tangent line to the curve f(x) = -x4 at x = 1. O T(X) = -1 + (-4)(x - 1) O T(X) = 1 + (4)(x- 1) O T(X) = -1 + (-4)(x - 4) O T(X) = 1 + (-4)(x- 1)Many things grow exponentially. The general formula for exponential growth is: g( t ) = Aert , where A is the starting value, r is the rate of growth and t is time. Assume that A = 1, and r = 1.05 (a 5% annual growth rate). g'( t ) = ret . What is the tangent line to the curve at t = 6? O T(t) = e6.3 - (1.05) e6.3 (x - 6) O T(t) = e6.3 + (1.05) e6.3 (x - 6) O T(t) = e6 + (1.06) e6 (x - 6) O T(t) = e6.3 + (1.06) e6.3 (x - 6)