Find the equation of the tangent line to the curvef (X) = -X- + 2xatx = 2. O T(x) = -2(x - 2) O T(X) = 2(x - 2) O T(x) = x2 - 1(x - 2) O T(x) = 2x - 1(x - 2)Find the equation of the tangent line to the curvef (X) = -X - 3x + 1 atx = 1. O T(X) = 3+5(x - 1) O T(x) = 3 -5(x - 1) O T(X) = 3+5(x+ 1) O T(x) = -3-5(x- 1)Which of the following is true? 0 If a differentiable function has the value h(5) = 4 and the derivative value h'(5) = -6 you can approximate the value of h(5.3). C) If a continuous function has the value h(5) = 4 you can approximate the value of h(5.3) using a tangent line approximation. Q You can get a good approximation of the value of h(3.1) if you know h(6) and h'(6). Q You can get a good approximation of the value of h(3.1) if you know h(5) and h'(5). Find the equation of the tangent line to the curve f ( X ) = VX. Assume f'( X ) = 21x at X = 4. O T(x) = 2+2( x-4) O T(x) = 2 - -(x-4) O T(X) = 2+ -(x-4) O T(X) = 2 - -(x-4)Find the equation of the tangent line to the curve f ( X ) = ex. Assume f '( x ) = ex at x = 2. O T( x) = e2 - e-(x-2) OT( x) =e-+e-( x - 2) O T( x ) = e-( x - 2) O T( x) = 2e-+ e2( x -2)A differentiable function has the value h(4) = 5 and the derivative value h' (4) = -6. Approximate the value of h(4.3). O 4.3 0 4 O 3.2 0 0A 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 0 2 O 1.9 Find the equation of the tangent line to the curve f(x) = x3 at x = 0. O T(x) = -1 O T(x) = 0 O T(x) = 1 O T(x) = -x Many things grow exponentially. The general formula for exponential growth is: g(t ) = Ae" , where A is the starting value, r is the rate of growth and t is time. Assume that A = 1, and r = 1.07 (a 7% annual growth rate) g ( t ) = rent . What is the tangent line to the curve at t = 6? O T(t) = e6 + (1.07) e6 (x - 6) O T(t) = e6.42 - (1.06) e6.42 (x - 6) O T(t) = @6.42 + (1.06) @6.42 (x - 6) O T(t) = e6.42 + (1.07) e6.42 (x - 6)