f (x) You are given h(x) = f(g(x)); p(x) = f(x)·g(x); q(x) = g(x) and the following values f(2) = 1, g(2) = 2, f'(2) = 2, g'(2) = 5 %3D %3D %3D Find h'(2), p'(2), аnd. q'(2)

f(3) = X f'(2) = 2 3 f(x) -1 f'(x) 7 g(x) Given that f(x) and g(x) are differentiable and that h(x) = f(x) · g(x) and k(x)=f(g(x)), use the values in the table to find f (3) and f'(2). 2 g'(x) -3 h'(x) 2 k'(x) -15

A function y = f(x) and an x-value xo are given. f(x) = x + Vr; xo = 1 (a) Find a formula for the slope of the tangent line to the graph of f at a general point xp. (b) Use the formula obtained in part (a) to find the slope of the tangent line for the given value of xo. a1) (a) Find a formula for the slope of the tangent line to the graph of fat a general point xp. The slope of the tangent line to f(x) at. xo is given by Def 2.1.1: Suppose that xo is in the domain of the function f. The tangent line to the curve y = f(x) at the point P(xp, f(x)) is the line with f(x) – f(x) . equation y – f(x0) = man(x – xo) where muan = lim provided the limit exists. x- xo f(x) – f(x0). Rewriting man = lim using f(x) = x + Vĩ, we get х — Хо (x+ Vã) – xo + Vxo man lim- x - x0 (x + Vx) – (xo + V) Man = lim х — Хо

Consider the function. F(x) = x³ – 6x² + 7 Find f'(x). f'(x) = Find f"(x). f"(x) = Find f"(-8) and f"(4). f"(-8) %D f"(4) Determine whether the function f(x) is concave up or concave down at the indicated points. (а) х%3D -8 O concave up O concave down (b) х%3D 4 O concave up O concave down