\f6) Suppose f (x) is a differentiable function such that f (1) = 7 and f'(1) = 2. Use a tangent line approximation to estimate f (0.8).\fQ) The table below gives specific values for a differentiable function ptx). Perform a tangent line approximation to estimate the yintercept in the graph of y = pux). Show the calculations that lead to your answer. x 1 3 4 6 9 p(x) 0.4 0.5 0.7 1.1 1.8 Which of the following is true? O You can get a good approximation of the value of h(3.1) if you know h(5) and h'(5). O You can get a good approximation of the value of h(3.1) if you know h(6) and h'(6). O 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). O If a continuous function has the value h(5) = 4 you can approximate the value of h(5.3) using a tangent line approximation.Find the equation of the tangent line to the curve f(x) = sin(x). Assume f '(x) = cos(x) at X = o T(x) = NA O T(x) = 1 O T(X) = 0 O T(x) = -1Find the equation of the tangent line to the curve f ( x ) = ex. Assume f'( x ) = e* at x = 2. O T( x) = 2e2+ e2( x - 2) O T( x) = e2 - e2(x-2) O T( x) = e-(x-2) OT( x) = e2+ 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 3.2A differentiable function has the value y(3) = 4 and the derivative value y'(3) = -2. Approximate the value of y(3.1). O 3.8 O 3.4 O 3.1 O -2\fFind the equation of the tangent line to the curve f(x) = -x3 + 1 at x = 1. O T(x) = 3(x - 1) O T(x) = -3(x - 1) O T(x) = 1(x - 3) O T(x) = -3Many things grow exponentially. The general formula for exponential growth is: g( 1') = A8\" . 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). 8% I) = re\" . What is the tangent line to the curve at t = 6? o T{t] = 95-3 {1.05) e5'3 (x 6) O T{t) = e5 + {1.06) e5 {x 5) O T{t) = e\" + (1.05} (25-3 [x 5} O T{t) = e53 + (1.05} e53 [x 5}