Differentiate the function after first rewriting the function in a different form. (Do not use the product or quotient rules. ) F(z) = A + Bz + Cz2 22 F'(Z) = -2AZ -3 - BZ-2 X Need Help? Read ItDifferentiate. At2 F(t) = - Bt5 + Ct9 2 at F'(t) = CO bt + ct XConsider the following. y = x\Find equations of the tangent line and normal line to the curve at the specified point. y: W, (1,0.25) x + 3 1 . tangent y = 16x+ 36 / normal 3/ = 16 The equation of motion of a particle is s = t - 4t + to - t, where's is in meters and t is in seconds. (Assume t 2 0.) (a) Find the velocity, v(t), and acceleration, a(t), as functions of t. v(t) = 413 - 912 + 2t-1 X a(t) = 1212 - 18+ + 2 X (b) Find the acceleration (in m/s=) after 1.2 s. a(1.2) = 20 x m/s2Suppose that f(4) = 3, g(4) = 4, f'(4) = -2, and g'(4) = 5. Find h'(4). (a) h(x) = 4f(x) + 5g(x) h' ( 4) = (b) h(x) = f(x)g(x) h' ( 4) = ( c) h ( x ) =_ f(x) g ( x ) h' ( 4) = (d) h(x) = g (x ) f (x) + g(x) h' ( 4) =If h(2) = 3 and h'(2) = -5, find d h(x ) dx X X = 2For what values of x does the graph of f(x) have a horizontal tangent? (Enter your answers as a comma-separated list. ) f( x) = x3 + 3x2 + x+5 X =